Summability of multi-dimensional Fourier series and Hardy spaces /

This is the first monograph which considers the theory of more-parameter dyadic and classical Hardy spaces. In this book a new application of martingale and distribution theories is dealt with. The theories of the multi-parameter dyadic martingale and the classical Hardy spaces are applied in Fourie...

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Bibliographic Details
Main Author: Weisz, Ferenc, 1964-
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Dordrecht ; Boston : Kluwer Academic, [2002]
Series:Mathematics and its applications (Kluwer Academic Publishers) ; volume 541.
Subjects:
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Multi-Dimensional Dyadic Hardy Spaces
  • Martingales and dyadic Hardy spaces
  • Inequalities with respect to Hardy spaces
  • Atomic decomposition
  • Interpolation between Hardy spaces
  • Bounded operators on H[subscript p]
  • Multi-Dimensional Classical Hardy Spaces
  • Distributions and Hardy spaces on R[superscript d]
  • Inequalities with respect to Hardy spaces
  • The atomic decomposition of H[superscript square subscript p]
  • The atomic decomposition of H[subscript p]
  • Interpolation between classical Hardy spaces
  • Bounded operators on H[subscript p]
  • Hardy spaces on T[superscript d]
  • Summability of D-Dimensional Walsh-Fourier Series
  • (C, [alpha]) and Riesz summations
  • Estimations of the (C, [alpha]) and Riesz kernels
  • The boundedness of the maximal operators on L[subscript p] spaces
  • The boundedness of the maximal operators on Hardy spaces
  • Some weak type inequalities for the maximal operators
  • Marcinkiewicz-Fejer summability of Walsh-Fourier series
  • Vilenkin system
  • The D-Dimensional Dyadic Derivative
  • The dyadic derivative and some estimations of the kernel function
  • The boundedness of I* on L[subscript p] spaces
  • The boundedness of I[subscript square] and I* on Hardy spaces
  • Vilenkin derivative
  • Summability of D-Dimensional Trigonometric-Fourier Series
  • [theta]-summability of Fourier series
  • Some summability methods
  • The boundedness of the maximal [theta]-operator on L[subscript p] spaces
  • The boundedness of the maximal [theta]-operator on Hardy spaces.