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
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 is assumed to satisfy the logarithmic Dini condition and the exponent of the power weight is related only to the value . 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.
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