Function spaces with variable exponents -- an introduction (Q2797810)

This is a survey article on function spaces with variable exponents. In the first chapter, the authors recall the definition and basic properties of the classical Lebesgue spaces \(L^p\), as well as the definition of the Hardy-Littlewood maximal operator and results on its boundedness on \(L^p\). Other classical concepts, for example \(A_p\)-weights, are also recalled.NEWLINENEWLINE Chapter 2 contains the definition of Lebesgue spaces with variable exponents and their basic properties (generalized Hölder inequality, completeness, duality results, etc.). The third chapter is devoted to the boundedness of the Hardy-Littlewood maximal operator on Lebesgue spaces with variable exponents.NEWLINENEWLINE In Chapter 4, various ``related topics'' are discussed, for instance, weighted Lebesgue spaces with variable exponents, fractional integrals and Calderón-Zygmund operators.NEWLINENEWLINE In the last chapter, the authors review some results on other function spaces with variable exponents, for example Campanato spaces, Morrey spaces and Hardy spaces with variable exponents.