Ukrainian Mathematical Bulletin

Volume 4, Issue 2, 2007 pp. 189-198.

Estimates for Integral Module of Continuity in Terms of the Sharp Maximal Function

Authors: Evgenii Yu. Leonchik
Author institution: I.I.Mechnikov Odessa National University, ul. Dvoryanskaya, 2, Odessa, 65082, Ukraine leonchik@ukr.net

Summary: In 1972 C. Fefferman and E. Stein have introduced a maximal function that measures the growth of local mean oscillations. Later, spaces that are associated with this functions were widely used in applications. In this paper, we find estimated for the integral module of continuity of functions in such spaces, and of functions that satisfy the generalized Poincare inequality.

Contents Full-Text PDF