𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A Generalization for Fourier Transforms of a Theorem due to Marcinkiewicz

✍ Scribed by Ferenc Weisz

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
143 KB
Volume
252
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

It is shown that the maximal operator of the Marcinkiewicz means of a tempered Ε½ 2 . Ε½ 2 . distribution is bounded from H R to L R for all pp F Ο± and, consep p 0 Ε½ . quently, is of weak type 1, 1 , where p -1. As a consequence we obtain a 0 generalization for Fourier transforms of a summability result due to Marcinkiewicz Ε½ 2 . and Zhizhiashvili, more exactly, the Marcinkiewicz means of a function f g L R 1 converge a.e. to the function in question. Moreover, we prove that the Ε½ 2 . Marcinkiewicz means are uniformly bounded on the spaces H R and so they p Ε½ . converge in the norm pp -Ο± . Similar results for the Riesz transforms are 0 also given.

πŸ“œ SIMILAR VOLUMES

A short proof for a generalization of Vi
A short proof for a generalization of Vizing's theorem
✍ Claude Berge; Jean Claude Fournier πŸ“‚ Article πŸ“… 1991 πŸ› John Wiley and Sons 🌐 English βš– 183 KB πŸ‘ 1 views

## Abstract For a simple graph of maximum degree Ξ”, it is always possible to color the edges with Ξ” + 1 colors (Vizing); furthermore, if the set of vertices of maximum degree is independent, Ξ” colors suffice (Fournier). In this article, we give a short constructive proof of an extension of these re

A Generalization of the Theorem of Hardy
A Generalization of the Theorem of Hardy: A Most General Version of the Uncertainty Principle for Fourier Integrals
✍ Christian Pfannschmidt πŸ“‚ Article πŸ“… 1996 πŸ› John Wiley and Sons 🌐 English βš– 406 KB πŸ‘ 1 views

N . WIENER remarked that a non-identically vanishing real function and its Fourier transform cannot both decay "very fast". It was HAR.DY who specified and proved this assertion in 1933. In the present paper Hardy's theorem will be generalized. Moreover, it will be shown that further weakening of th

A generalization of a conservativity the
A generalization of a conservativity theorem for classical versus intuitionistic arithmetic
✍ Stefano Berardi πŸ“‚ Article πŸ“… 2004 πŸ› John Wiley and Sons 🌐 English βš– 124 KB

## Abstract A basic result in intuitionism is Ξ ^0^~2~‐conservativity. Take any proof __p__ in classical arithmetic of some Ξ ^0^~2~‐statement (some arithmetical statement βˆ€__x__.βˆƒ__y__.__P__(__x, y__), with __P__ decidable). Then we may effectively turn __p__ in some intuitionistic proof of the same