Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Restrictions of $L^{p}$ transforms


Author: Louis Pigno
Journal: Proc. Amer. Math. Soc. 29 (1971), 511-515
MSC: Primary 42.40; Secondary 46.00
DOI: https://doi.org/10.1090/S0002-9939-1971-0279531-5
Erratum: Proc. Amer. Math. Soc. 48 (1975), 515.
MathSciNet review: 0279531
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let G be a locally compact abelian group with dual $\Gamma$, E a subset of $\Gamma$, and $\phi$ a complex-valued function defined on $\Gamma$. Assume $\phi$ has $\sigma$-compact support. In this paper we prove that $\phi$ is a multiplier of type $({L^1},{L^{{p_1}}} \cap {L^{{p_2}}},E)\;(1 \leqq {p_1} \leqq 2,1 < {p_2} \leqq \infty )$ if and only if $\phi = \hat f$ a.e. on E for some $f \in {L^{{p_1}}}(G) \cap {L^{{p_2}}}(G)$. We give applications of this result to the problems of restrictions, uniqueness, inversion and characterization of ${L^p}$ transforms.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42.40, 46.00

Retrieve articles in all journals with MSC: 42.40, 46.00


Additional Information

Keywords: Multiplier, quotient space, regular Toeplitz summation matrix
Article copyright: © Copyright 1971 American Mathematical Society