On restricted weak type (1,1): The continuous case-Reference-Cited by-同舟云学术

On restricted weak type (1,1): The continuous case

Published:2004-06-02 Issue:1 Volume:133 Page:185-190
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Hagelstein Paul,Jones Roger

Abstract

Let T \mathbb {T} denote the unit circle. An example of a sublinear translation-invariant operator T T acting on L 1 ( T ) L^{1}\left (\mathbb {T}\right ) is given such that T T is of restricted weak type ( 1 , 1 ) (1,1) but not of weak type ( 1 , 1 ) (1,1) .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2005-133-01/S0002-9939-04-07530-6/S0002-9939-04-07530-6.pdf

Reference7 articles.

1. On restricted weak type (1,1); the discrete case;Akcoglu, Mustafa;Israel J. Math.,2001

2. Pure and Applied Mathematics, No. 70;Brown, James R.,1976

3. Ergodic theory and translation-invariant operators;Calderón, A.-P.;Proc. Nat. Acad. Sci. U.S.A.,1968

4. A theory of entropy in Fourier analysis;Fefferman, Robert A.;Adv. in Math.,1978

5. On restricted weak type (1,1);Moon, K. H.;Proc. Amer. Math. Soc.,1974

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