IJPAM: Volume 51, No. 4 (2009)

ON HILBERT TRANSFORM IN CONTEXT OF
LOCALLY COMPACT ABELIAN GROUPS

A.R. Mirotin
Department of Mathematics
Skoryna Gomel State University
104, Sovietskaya, Gomel, 246019, BELARUS
e-mail: [email protected]


Abstract.The aim of the paper is to obtain generalizations of M. Riesz's Theorem on the Hilbert transform to compact and locally compact Abelian groups with some fixed subsemigroup of the dual group. Application to generalized Toeplitz operators is given.

Received: March 20, 2008

AMS Subject Classification: 43A32, 43A17

Key Words and Phrases: Hilbert transform, conjugate function, M. Riesz's inequality, Toeplitz operator, locally compact Abelian group, semigroup

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 51
Issue: 4