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.

• function spaces
• Morrey spaces
• Lebesgue spaces
• Lorentz sequence spaces
• hardy type inequalities
• integral operators
• Sobolev embeddings
• harmonic analysis

• Department of Mathematics, South Asian University, New Delhi, India

  Pankaj Jain

• Faculty of Mathematics & Computer Science, Friedrich Schiller University Jena, Jena, Germany

  Hans-Jürgen Schmeisser

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).

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