✦ LIBER ✦

On Extrapolation Spaces and a.e. Convergence of Fourier Series

✍ Scribed by M. Milman

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 441 KB
Volume: 80
Category: Article
ISSN: 0021-9045
DOI: 10.1006/jath.1995.1002

No coin nor oath required. For personal study only.

✦ Synopsis

A new, unified approach to recent end point estimates for the maximal operator of partial sums of Fourier series is obtained through the use of extrapolation theory. The method involves characterizing certain extrapolation spaces associated with scales of Lorentz-Zygmund spaces. ""1995 Academic Press. Inc.

📜 SIMILAR VOLUMES

Effective Fine-convergence of Walsh-Four

Effective Fine-convergence of Walsh-Fourier series

✍ Takakazu Mori; Mariko Yasugi; Yoshiki Tsujii 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 182 KB

## Abstract We define the effective integrability of Fine‐computable functions and effectivize some fundamental limit theorems in the theory of Lebesgue integrals such as the Bounded Convergence Theorem, the Dominated Convergence Theorem, and the Second Mean Value Theorem. It is also proved that th

On the convergence of Fourier series of

On the convergence of Fourier series of computable Lebesgue integrable functions

✍ Philippe Moser 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 130 KB

This paper studies how well computable functions can be approximated by their Fourier series. To this end, we equip the space of L p -computable functions (computable Lebesgue integrable functions) with a size notion, by introducing L p -computable Baire categories. We show that L p -computable Bair

Mean and Almost Everywhere Convergence o

Mean and Almost Everywhere Convergence of Fourier–Neumann Series

✍ Óscar Ciaurri; José J. Guadalupe; Mario Pérez; Juan L. Varona 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 162 KB

On Fourier Multipliers of Homogeneous Be

On Fourier Multipliers of Homogeneous Besov Spaces

✍ Takahiro Mizuhara 📂 Article 📅 1987 🏛 John Wiley and Sons 🌐 English ⚖ 270 KB 👁 1 views

Complementary Spaces and Multipliers of

Complementary Spaces and Multipliers of Double Fourier Series for Functions of Bounded Variation

✍ S. Baron; E. Liflyand; U. Stadtmüller 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 110 KB

Complementary spaces for Fourier series were introduced by G. Goes and generalized by M. Tynnov. In this paper we investigate a notion of complementary space for double Fourier series of functions of bounded variation. Various applications are given.

On the Riemann Summability of Fourier In

On the Riemann Summability of Fourier Integrals and Real Hardy Spaces

✍ Ferenc Móricz 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 213 KB 👁 2 views

We consider the Riemann means of single and multiple Fourier integrals of functions belonging to L 1 or the real Hardy spaces defined on IR n , where n ≥ 1 is an integer. We prove that the maximal Riemann operator is bounded both from H 1 (IR) into L 1 (IR) and from L 1 (IR) into weak -L 1 (IR). We