Miroslav Krbec

Mathematical Institute
Academy of Sciences of the Czech Republic

List of publications

Monographs:

Weighted Inequalities in Lorentz and Orlicz Spaces.
World Scientific, Singapore-New Jersey-London-Hong Kong 1991,
233 pp. (Together with V. Kokilashvili.)

Weight Theory for Integral Transforms on Spaces of Homogeneous Type.
Addison-Wesley, Pitman Monographs and Surveys in Pure and Applied Mathematics 92, Harlow 1998, 410 pp.
(Together with I. Genebashvili, A. Gogatishvili and V. Kokilashvili.) 

Unilateral Contact Problems: Variational Methods and Existence Theorems.
Pure and Applied Mathematics Vol. 270. Chapman & Hall/CRC, Boca Raton 2005, 398 pp..
(Together with C. Eck, J. Jarušek.}

Papers:

On L^p-estimates for solutions of elliptic boundary value problems.
Comment. Math. Univ. Carolinae 17(1976), 363-375.

Boundary value problem with bounded nonlinearity and general null-space of the linear part.
Math. Z. 155(1977), 129-138.
(Together with S. Fučík.)

Modular interpolation spaces I.
Z. Anal. Anwendungen 1(1982), 25-40.

Interpolation in Orlicz and Sobolev-Orlicz spaces.
In: Proceedings of the Conference on Operator Theory and Partial Differential Equations.
Austr. Nat. Univ., Canberra 1983, 109-123.

On anisotropic imbeddings.
Comment. Math. Univ. Carolinae 25(1985), 473-481.

Weighted inequalities for Riesz potentials and fractional maximal functions in Orlicz spaces} (Russian).
Dokl. Akad. Nauk SSSR 283(1985), 280-283. (English transl.: Soviet Math. Dokl. 32(1985), 70-73.)
(Together with V. Kokilashvili.)

An integral characterization of zero traces in nonreflexive Sobolev type spaces.
Coll. Math. Soc. János Bolyai 49(1985), 525-529.

On boundedness of anisotropic fractional order maximal functions and potentials in weighted Orlicz spaces} (Russian).
Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 82(1986), 106-115.
(Together with V. Kokilashvili.)

Two weight weak type inequalitites for the maximal function in the Zygmund class.
In: Lecture Notes Math. Vol. 1302, Function Spaces and Applications, US-Swedish Seminar Lund, June 1986.
Springer-Verlag, Berlin-Heidelberg-New York 1988, pp. 317-320.

Weighted norm inequalities in Orlicz spaces.
In: Function spaces, differential operators and nonlinear analysis.
Research Notes in Mathematics Series, Longman Sci. & Tech., Harlow 1989, pp. 77-88.

Maximal functions in Phi(L) classes and Carleson measures.
Soobshch. Akad. Nauk Gruzin. SSR 137(1990), 269-271.
(Together with V. Kokilashvili.)

Maximal functions in Phi(L) classes (Russian).
Dokl. Akad. Nauk SSSR 314,3(1990), 534-536.
(Together with A. Gogatishvili and V. Kokilashvili.)

On imbeddings between weighted Orlicz classes.
Z. Anal. Anwendungen 10(1991), 107-117.
(Together with L. Pick.)

Imbedding theorems for weighted Orlicz-Sobolev spaces.
J. London Math. Soc. (2)46(1992), 543-556.
(Together with B. Opic and L. Pick.)

Maximal functions, Phi(L) classes and Carleson measures.
Proc. Georg. Acad. Sci. Math. 102(1993), 85-96.
(Together with A. Gogatishvili and V. Kokilashvili.)

On two limiting cases of Sobolev imbeddings.
Houston J. Math. 21(1995), 119-128.
(Together with D. E. Edmunds.)

Inequalities for classical operators in Orlicz spaces.
In: Fourier Analysis and Partial Differential Equations,
CRC Press, Boca Racon 1995, 211-226.

Limiting imbeddings. The case of missing derivatives.
Ricerche Mat. XLV(1996), 423-447.
(Together with H.-J. Schmeisser.)

Extrapolation of reduced imbeddings. In: Function Spaces,
Differential Operators and Nonlinear Analysis,
Proc. Conf. held in Paseky nad Jizerou 1995, pp. 71-88.
(Together with H.-J.Schmeisser.)

On imbeddings between weighted Orlicz-Lorentz spaces.
Georgian Math. J. 4,2(1997), 117-128.
(Together with J. Lang.)

Indices of Orlicz spaces and some applications.
Comment. Math. Univ. Carolinae 38,3(1997), 433-451.
(Together with A. Fiorenza.)

Embeddings of weighted Sobolev spaces in the borderline case.
Real Anal. Exchange 23,2(1997-98), 395-420.
(Together with T. Schott.)

Extrapolation of Sobolev imbeddings.
Collectanea Math. 48(4,5,6)(1997), 601-617.

A formula for the Boyd indices in Orlicz spaces.
Funct. et Approximatio 26(1998), 173-179.
(Together with A. Fiorenza.)

Superposition of imbeddings and Fefferman's inequality.
Boll. Un. Mat. Ital., Sez. B, Artic. Ric. Mat. 8,2(1999), 629-637.
(Together with T. Schott.)

The trace inequality and some applications.
Le Matematiche LIV(1999), 95-109.

On decomposition in exponential Orlicz spaces.
Math. Nachr. 213(2000), 77-88.
(Together with D. E. Edmunds.)

On the domain and range of the maximal operator.
Nagoya Math. J. 158(2000), 43-61.
(Together with A. Fiorenza.)

On some fundamental properties of the maximal operator.
In: Function Spaces and Applications,
Narosa Publ. House, New Delhi 2000, pp. 69-81.
(Together with A. Fiorenza.)

Weighted exponential inequalities.
Georg. Math. J. 8(2001), 69-86.
(Together with H. Heinig and R. Kerman.)

Imbeddings of Brezis-Wainger type. The case of missing derivatives.
Proc. Roy. Soc. Edinburgh, 131A(2001), 1-34.
(Together with H.-J. Schmeisser.)

Decomposition and Moser's lemma.
Rev. Mat. Complutense 9(2002), 1-18.
(Together with D.E. Edmunds.)

On optimal decomposition in Zygmund spaces.
Georgian Math. J. 9(2002), 271-286.
(Together with A. Fiorenza.)

Localization and extrapolation in Lorentz-Orlicz spaces.
In: Function Spaces, Interpolation  Theory and Related Topics.
Proceedings of the conference held in Lund (Sweden), August 17-22, 2001, in honour of
Jaak Peetre on his 65th birthday (A. Kufner, L.E. Persson, G. Sparr, M. Engliš, eds.).
de Gruyter, Berlin 2002, 389-401.
(Together with D. Cruz-Uribe, SFO.)

Conical differentiability for evolution variational inequalities.
 J. Diff. Equations 193( 2003), 131-146.
(Together with J. Jarusek, M. Rao and J. Sokolowski.)

Variations on Yano's extrapolation theorem.
Rev. Mat. Complut. 18(2005), 111-118.
(Together with D. E. Edmunds.)

Refined limiting imbeddings for Sobolev spaces of vector-valued functions.
J. Funct. Anal. 227(2005), 372-388.
 (Together with H.-J. Schmeisser.)

On extrapolation blowups in the $L_p$ scale.
J. Inequal. Appl. vol. 2006, 1-9.
(Together with C. Capone and A. Fiorenza.)

A limiting case of the uncertainty principle.
Proceedings of Equadiff 11, Proceedings of minisymposia and contributed talks,
July 25-29, 2005, Bratislava (eds.: M. Fila et al.), Bratislava 2007, pp. 181-187.
(Together with H.-J. Schmeisser.)

Critical imbeddings with multivariate rearrangements.
Studia Math. 181(2007), 255-284.  
(Together with H.-J. Schmeisser.)

On non-effective weights in Orlicz spaces.
Indag. Mathem., N.S. 18 (2) (2007), 215-231.
(Together with H.~Hudzik.)
 
A weighted Lq-approach to Oseen flow around a rotating body.
Math. Models Methods Appl. Sci. 31(2007), 551-574.
(Together with  R. Farwig and Š. Nečasová.)

 A weighted $L^q$-approach to Stokes flow around a rotating body.
Ann. Univ. Ferrara Sez. VII Sci. Mat. 54 (2008), no. 1, 61-84.
(Together with  R. Farwig and Š. Nečasová.)

On the Trace Space of a Sobolev Space with a Radial Weight.
J. Funct. Spaces Appl. 6(2008), 259-276.
(Together with  H. Abels and K. Schumacher.)

Gagliardo-Nirenberg inequalities in regular Orlicz spaces involving nonlinear expressions.
J. Math. Anal. Appl. 362, No. 2, (2010), 460-470 .
(Together with A. Kałamajska.)

Moduli and characteristics of monotonicity in some Banach lattices. To appear in J Fixed Point Theory Appl. (Together with P. Foralewski, H. Hudzik and R. Kaczmarek.)

On weighted critical imbeddings of Sobolev spaces. To appear in Math. Z. (Together with D.E. Edmunds and H. Hudzik.)




Proceedings papers (surveys, amalgams):

Interpolation in Sobolev-Orlicz spaces (Russian). Sbornik 7.
sovetskogo-cechoslovackogo seminara "Primenenija metodov teorii funkcij
i funkcional'nogo analiza k zadacam matematiceskoj fiziki",
Yerevan 1981, 147-180.

An imbedding theorem for Sobolev-Orlicz spaces via interpolation.
In: Constructive Theory of Functions '81,
Proc. Int. Conf. Varna '81, Publ House Bulg. Acad. Sci., Sofia 1983, pp. 393-395.

On the boundedness of Riesz potentials and fractional maximal functions in weighted Orlicz spaces.
In: Proceedings of the International Conference on Constructive Theory of Functions, Varna '84.
Publ. House Bulg. Acad. Sci., Sofia 1984, 468-472
(Together with V. Kokilashvili.)

A characterization of functions with zero traces.
In: Constructive Theory of Functions '87,
Proc. Int. Conf. Varna '87, Publ House Bulg. Acad. Sci. Sofia 1988.

Some recent results on Hardy type operators in weighted function spaces and related topics.
In: Function Spaces, Differential Operators and Nonlinear Analysis.
Teubner-Texte zur Mathematik, Band 133 (Schmeisser/Triebel, Eds.).
B. G. Teubner Verlagsgesellschaft, Stuttgart-Leipzig 1993, pp. 158-184.
(Together with B. Opic, L. Pick and J. Rákosník.)

On extrapolation of Sobolev and Morrey type imbeddings.
In Hudzik, H. et al. Function spaces. Proceedings of the 5th international conference,
Poznan, Poland, August 28-September 3, 1998
Lect. Notes Pure Appl. Math. vol.~213, New York: Marcel Dekker, Inc., 2000, p. 297-321.
(Together with H.-J. Schmeisser.)

Extrapolation. Recent results and challenges.
In: Rakosnik et al. Function Spaces, Differential Operators and Nonlinear Analysis.
Proceedings of  Conf. held in Milovy, May 28-June 2, 2004.

Preprints:

Sobolev-Orlicz trace spaces. Research Report ANU,
Centre for Mathematical Analysis, Canberra 1983.

Some imbedding theorems for anisotropic Sobolev spaces.
Research Report ANU, Centre for Mathematical Analysis, Canberra 1983.

Weighted norm inequalities for fractional order maximal functions and Riesz potentials in Orlicz spaces.
Preprint no. 5, Math. Inst. Czech. Acad. Sci., Prague 1984.
(Together with V. Kokilashvili).

On imbeddings between weighted Orlicz classes.
Preprint no. 37, Math. Inst. Czech. Acad. Sci., Prague 1988.
(Together with L. Pick.)

Imbedding theorems for weighted Orlicz-Sobolev spaces.
Preprint no. 64, Math. Inst. Czech. Acad. Sci., Prague 1990.
(Together with B. Opic and L. Pick.)

Weighted exponential inequalities.
Preprint no. 79, Math. Inst. Czech. Acad. Sci., Prague 1992.
(Together with H. Heinig and R. Kerman.)

Some recent results on Hardy type operators in weighted function spaces and related topics.
Preprint No. 88, Inst. Math. Acad. Sci. Czech Rep., Prague 1993.
(Together with B. Opic, L. Pick and  J. Rákosník.)

On two limiting cases of Sobolev imbeddings.
Preprint No. 89, Inst. Math. Acad. Sci. Czech Rep., Prague 1994.
(Together with D. E. Edmunds.)

On imbeddings between weighted Orlicz-Lorentz spaces.
Preprint No. 98, Inst. Math. Acad. Sci. Czech Rep., Prague 1994.
(Together with J. Lang.)

Indices of Orlicz spaces.
Preprint No. 10, Universita degli Studi di Napoli, "Federico II", 1995.
(Together with A. Fiorenza.)

Limiting imbeddings---the case of missing derivatives.
Preprint No. 103, Math. Inst. Acad. Sci. Czech Rep., Prague 1995.
(Together with H.-J.Schmeisser.)

Imbeddings of weighted Sobolev spaces in the borderline case.
Preprint No. 104, Inst. Math. Acad. Sci. Czech Rep., Prague 1995.
(Together with T. Schott.)

Indices of Orlicz spaces and some applications.
Preprint No. 115, Inst. Math. Acad. Sci. Czech Rep., Prague 1995.
(Together with A. Fiorenza.)

On decomposition in exponential Orlicz spaces.
Research Report No. 96/25, University of Sussex, Brighton 1996.
(Together with D. E. Edmunds.)

On the domain and range of the maximal operator.
Preprint No. 122, Math. Inst. Acad. Sci. Czech Rep., Prague 1997.
(Together with A. Fiorenza.)

Superposition of imbeddings and Fefferman's inequality.
Preprint No. 127, Math. Inst. Acad. Sci. Czech Rep., Prague 1998.
(Together with T. Schott.)

Decomposition and Moser's lemma.
Research report No:2001-02,
Centre for Mathematical Analysis and Its Applications,
University of Sussex at Brighton, Brighton 2001.
(Together with D. E. Edmunds.)

Refined limiting imbeddings for Sobolev spaces of vector-valued functions.
Jenaer Schriften zur Math. und Inf., Math/Inf/03/04., Jena 2004.
(Together with H.-J. Schmeisser.)

Variations on Yano's extrapolation theorem
Research report No: 2004-01, Centre for Mathematical Analysis and Its Applications,
University of Sussex at Brighton, Brighton 2004.
(Together with D. E. Edmunds.)

On extrapolation blowups in the $L_p$ scale.
Preprint No. RT 285/04,  Istituto per le Applicazioni del Calcolo "Mauro Picone"  2004.
(Together with C. Capone and A. Fiorenza.)

On non-effective weights in Orlicz spaces.
Report No. 122/2005, Faculty of Math. and Comp. Science UAM, Poznan 2005.
(Together with H. Hudzik.)  
 pdf file here.

Critical imbeddings with multivariate rearrangements.  
Jenaer Schriften zur Math. und Inf., Math/Inf/04/06., Jena 2006, 37 pp.
(Together with H.-J. Schmeisser.)
pdf file here

Dimension-free imbeddings of Sobolev spaces. Preprint, Jena 2010. 
 (Together with H.-J. Schmeisser.)


Editorial activities:
Proceedings of the Spring School "Nonlinear Analysis, Function Spaces and Applications 3".
Teubner, Leipzig 1986.
(Together with A. Kufner and J. Rákosník.)

Proceedings of the Spring School "Nonlinear Analysis, Function Spaces and Applications 4".
Teubner, Leipzig 1990.
(Together with A. Kufner, B. Opic and J. Rákosník.)

Proceedings of the Spring School "Nonlinear Analysis, Function Spaces and Applications 5".
Prometheus, Prague 1994.
(Together with A. Kufner, B. Opic and J. Rákosník.)

Proceedings of the Spring School "Nonlinear Analysis, Function Spaces and Applications 6".
Math. Inst. Acad. Sci. Czech Rep., Prague 1998.
(Together with A. Kufner.)

Abstracts, Posters, Enlarged Abstracts. Equadiff 10, Math. Inst. Prague 2001.
(Together with K. Horák.)

Equadiff 10, CD ROM Proceedings. Masaryk University Brno 2002.
(Together with J. Kuben and J. Vosmanský.)