V. A. Andrienko, “Embedding of $H_p^\omega$ in the class $e^L$”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, Number 3,Pages 3

Embedding of $H_p^\omega$ in the class $e^L$

V. A. Andrienko

Chair of Mathematical Analysis, Odessa National University, Odessa, Ukraine

Abstract: We obtain the necessary conditions for the embedding $H_p^\omega\subset e^L$ ($1\le p<\infty$) with convex modulus of continuity $\omega$ in terms of this modulus. In the case $p=1$ these conditions are also sufficient.

Keywords: modulus of continuity, decreasing rearrangement, embedding in the class $\varphi(L)$.

UDC: 517.5

Received: 08.11.2007