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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| Format: | eBook |
| Language: | English |
| Published: |
Dordrecht ; Boston :
Kluwer Academic,
[2002]
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| 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.