Recent Publications

Littlewood's law of miracles:"... Each person experiences about 30,000 events per day. A miracle - an event with special significance - has a probability of one chance in a million. This works out to about one miracle per person per month"

Preprints available (you can retrieve copies from the Arxiv)

2010

Isoperimetric Hardy type and Poincare inequalities on metric spaces Around the Research of V Maz'ya, Vol I. Function Spaces, pp. 285-298, Springer (2010) (jointly with Joaquim Martin)

2009

Pointwise Symmetrization Inequalities for Sobolev functions and applications, preprint, 2009 (jointly with Joaquim Martin)

Isoperimetry and Symmetrization for Sobolev spaces on metric spaces, Comptes Rendus Mathematique 347 (2009), 627-630(jointly with Joaquim Martin).

Symmetrization and sharp Sobolev inequalities in metric spaces (jointly with Jan Kalis), Revista Matematica Complutense 22 (2009), no. 2, 499Ð515

Isoperimetry and Symmetrization for Logarithmic Sobolev inequalities, (jointly with Joaquim Martin), Journal of Functional Analysis 256 (2009), 149-178.

Addendum to Isoperimetry and Symmetrization for Logarithmic Sobolev inequalities (January 2009), Arxiv.org (jointly with Joaquim Martin)

2008

Self Improving Sobolev-Poincar\'{e} Inequalities, Truncation and Symmetrization, Potential Analysis 29 (4), 391-408 (jointly with Joaquim Martin).

Book: Topics in Classical Analysis and Applications in Honor of Daniel Waterman (Edited jointly with L. DeCarli and K. Kazarian), World Scientific, 2008.

An abstract Coifman-Rochberg-Weiss commutator theorem,in Topics in Classical Analysis and Applications in Honor of Dan Waterman, World Scientific, 2008, pp 141-160 (jointly with J. Martin).

2007

Interpolation Theory and Applications: A conference in honor of Michael Cwikel, (Edited jointly with Laura De Carli), Contemporary Mathematics 445 (2007); 357 pp

Weakly rearrangement invariant spaces and approximation by largest elements (jointly with Björn Jawerth), Contemporary Mathematics 445 (2007), 103-110.

A note on Sobolev inequalities and limits of Lorentz spaces, (jointly with J. Martin), Contemporary Mathematics 445 (2007), 237-245.

Michael Cwikel: Mathematician (jointly with Richard Rochberg), Contemporary Mathematics 445 (2007), 1-9.

Sobolev Inequalities: Symmetrization and Self Improvement via Truncation, Journal of Functional Analysis 252 (2) (2007), 677-695 (jointly with Joaquim Martin and Evgeniy Pustylnik)

(2007 Paseky Lectures)Optimization, Image Processing and Interpolation Theory, [in Function Spaces, Inequalities and Interpolation, Charles University, Paseky 2007], (jointly with Björn Jawerth)

On the Brudnyi-Krugljak duality theory of spaces formed by the K-method of interpolation (jointly with R. Kerman and G. Sinnamon), Revista Matematica Complutense 20 (2007), no. 2, 367-389.

Higher order symmetrization inequalities and applications (jointly with J. Martin), Journal of Mathematical Analysis and Applications 330 1 (2007), 91-113

Sharp Gagliardo-Nirenberg inequalities via Symmetrization, (jointly with J. Martin), Mathematical Research Letters 14 (2007), 49-62.

2006

Extrapolation methods and Rubio de Francia's extrapolation theorem (jointly with J. Martin), Advances in Mathematics 201 (2006), 209-262. Review #1, Review #2

Weighted norm inequalities and indices, Journal of Function spaces and Applications 4 (2006), 43-71 (jointly with J. Martin). Review

Symmetrization inequalities and Sobolev embeddings, (jointly with J. Martin), Proceedings of the American Mathematical Society 134 (2006), 2335-2347.

2005

Extrapolation Theory: New Results and Applications, (jointly with G. Karadhzov), Journal of Approximation Theory 133 (2005), 38-99, Review#1, Review #2

Limits of higher order Besov spaces and sharp reiteration theorems, (jointly with G. Karadzhov and J. Xiao), Journal of Functional Analysis 221 (2005), 323-339, Review.

Notes on limits of Sobolev spaces and the continuity of Interpolation Scales Transactions of the American Mathematical Society 357 (2005), 3425-3442, Review.