Journal of Function Spaces

Journal of Function Spaces / 2003 / Article

Open Access

Volume 1 |Article ID 932158 | https://doi.org/10.1155/2003/932158

Vakhtang Kokilashvili, Stefan Samko, "Singular integrals and potentials in some Banach function spaces with variable exponent", Journal of Function Spaces, vol. 1, Article ID 932158, 15 pages, 2003. https://doi.org/10.1155/2003/932158

Singular integrals and potentials in some Banach function spaces with variable exponent

Academic Editor: Alois Kufner
Received01 Dec 2002

Abstract

We introduce a new Banach function space - a Lorentz type space with variable exponent. In this space the boundedness of singular integral and potential type operators is established, including the weighted case. The variable exponent p(t) is assumed to satisfy the logarithmic Dini condition and the exponent β of the power weight ω(t)=|t|β is related only to the value p(0). The mapping properties of Cauchy singular integrals defined on Lyapunov curves and on curves of bounded rotation are also investigated within the framework of the introduced spaces.

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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