Four Lectures on Real HP Spaces

This book introduces the real variable theory of "HP" spaces briefly and concentrates on its applications to various aspects of analysis fields. It consists of four chapters. Chapter 1 introduces the basic theory of Fefferman Stein on real "HP" spaces. Chapter 2 describes the atomic decomposition theory and the molecular decomposition theory of real "HP" spaces. In addition, the dual spaces of real "HP" spaces, the interpolation of operators in "HP" spaces, and the interpolation of...
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This book introduces the real variable theory of "HP" spaces briefly and concentrates on its applications to various aspects of analysis fields. It consists of four chapters. Chapter 1 introduces the basic theory of Fefferman Stein on real "HP" spaces. Chapter 2 describes the atomic decomposition theory and the molecular decomposition theory of real "HP" spaces. In addition, the dual spaces of real "HP" spaces, the interpolation of operators in "HP" spaces, and the interpolation of "HP" spaces are also discussed in Chapter 2. The properties of several basic operators in "HP" spaces are discussed in Chapter 3 in detail. Among them, some basic results are contributed by Chinese mathematicians, such as the decomposition theory of weak "HP" spaces and its applications to the study on the sharpness of singular integrals, a new method to deal with the elliptic Riesz means in "HP" spaces, and the transference theorem of "HP"-multipliers etc. The last chapter is devoted to applications of real "HP" spaces to approximation theory.
Contents: "Real Variable Theory of HP (Rn)""Spaces: "Definition of "HP" "(Rn) Spaces"Non-Tangential Maximal FunctionsGrand Maximal Functions"Decomposition Structure Theory of HP (Rn) Spaces: "AtomDual Spaces of "H"1 (Rn)Atom DecompositionDual Space of "HP" (Rn)Interpolation of OperatorsInterpolations of "HP" SpacesWeak "HP" SpacesMoleculeMolecule DecompositionApplications to the Boundedness of Operators"Applications to Fourier Analysis: "Fourier TransformFourier MultiplierRiesz Potential OperatorsSingular Integral OperatorsBochner-Riesz MeansTransference Theorems of "HP"-Multipliers"Applications to Approximation Theory: "K Functional"HP"-Multiplier and Jackson-Type Inequality"HP"-Multiplier and Bernstein Type InequalityApproximation by Bochner-Riesz Means at Critical Index
Readership: Mathematicians.
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