Singular integrals and potentials in some Banach function spaces with variable exponent
By V. Kokilashvili, S. Samko. 2003
50 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/07bc69de89383d51734625c11a4e319834801a6e
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In Applied Mathematics
- A. Meskhi
- V. Kokilashvili
- S. Samko
- Lars Diening
- Ovidiu Munteanu
- Jiaping Wang
- Kwok-Pun Ho
- S. Umarkhadzhiev
In Mathematical Physics
Citations in the corpus
- On the Boundedness and Compactness of Weighted Hardy Operators in Spaces 𝐿𝑝(𝑥) (2005, background): “Finally we mention that the boundedness of Hv,w and Hv,w in weighted spaces L for some power weights v and w is established in [15]–[16].”