Function Spaces and Inequalities

This book features original research and survey articles on the topics of function spaces and inequalities. It focuses on (variable/grand/small) Lebesgue spaces, Orlicz spaces, Lorentz spaces, and Morrey spaces and deals with mapping properties of operators, (weighted) inequalities, pointwise multipliers and interpolation. Moreover, it considers Sobolev-Besov and Triebel-Lizorkin type smoothness spaces. The book includes papers by leading international researchers, presented at the International Conference on Function Spaces and Inequalities, held at the South Asian University, New Delhi, India, on 11-15 December 2015, which focused on recent developments in the theory of spaces with variable exponents. It also offers further investigations concerning Sobolev-type embeddings, discrete inequalities and harmonic analysis. Each chapter is dedicated to a specific topic and written by leading experts, providing an overview of the subject and stimulating future research.

Autorentext

PANKAJ JAIN is associate professor of Mathematics at the South Asian University, New Delhi, India. With over 27 years of teaching experience, Dr Jain has taught several courses in pure and applied mathematics both at undergraduate and postgraduate levels. His research interests include the theory of function spaces, integral inequalities of Hardy type and Fourier analysis. He has authored more than 50 research papers in several respected international journals. Dr Jain has been involved in 23 collaborations, including 12 from outside India. Dr Jain has received grants from various agencies in India and abroad in connection with research projects, attending international conferences and collaborating with foreign mathematicians. This includes the BOYSCAST fellowship of DST visiting Sweden, the Royal Society (London) Exchange Programme visiting the U.K. three times and very recently the Indo-Russian S&T project.

HANS-JÜRGEN SCHMEISSER is professor of Analysis at the Friedrich Schiller University of Jena, Germany. His research fields include the theory of function spaces as well as Fourier analysis and approximation theory. He has published a joint monograph with Hans Triebel on Topics in Fourier Analysis and Function Spaces and about 60 research papers with 12 coauthors. He is one of the organisers of the international conference series on Function Spaces, Differential Operators and Nonlinear Analysis (FSDONA). His research has received several grants from the German Research Foundation (DFG).

Inhalt
Fernando Cobos and Luz M. Fernández-Cabrera, The fundamental function of certain interpolation spaces generated by N-tuples of rearrangement-invariant spaces.- Douadi Drihem, Sobolev embeddings for Herz-type Triebel-Lizorkin spaces.- M. L. Goldman, Order sharp estimates for monotone operators on Orlicz--Lorentz classes.- D. I. Hakim and Yosihiro Sawano, Complex interpolation of Morrey spaces .- Dorothee D. Haroske and Hans-Juergen Schmeisser, Gagliardo-Nirenberg inequalities for spaces with dominating mixed derivatives.- Pankaj Jain, Monika Singh and Arun Pal Singh, Recent trends in the theory of grand Lebesgue spaces. Agnieszka Kalamajska and Iwona Skrzypczak, On certain new method to construct weighted Hardy-type inequalities and its application to the sharp Hardy-Poincare' inequalities.- Henning Kempka, Intrinsic characterization and the extension operator in variable exponent function spaces on special Lipschitz domains.- V. Kokilashvili and A. Meskhi, The boundedness of sublinearoperators in weighted Morrey spaces defined on spaces of homogeneous type.- Romesh Kumar, A.K. Sharma, S. Dubey and S. Wazir, Essentially algebraic composition operators on Lorentz sequence spaces with a weight.- Santosh Kumari, Higher dimensional Hardy-type inequalities.- Jan Lang, Osvaldo Mendez and Behzad Rouhani, Recent advances on generalized trigonometric systems in higher dimensions.- Eiichi Nakai, Pointwise multipliers on Musielak-Orlicz-Morrey spaces.- Hans Triebel, The Fatou property of function spaces, heat kernels, admissible norms and mapping properties.- Dachun Yang and Wen Yuan, A survey on some variable function spaces