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

Vakhtang Kokilashvili | Zendy; Stefan Samko | Zendy

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

Author(s) -

Vakhtang Kokilashvili,

Stefan Samko

Publication year - 2003

Publication title -

journal of function spaces

Language(s) - English

Resource type - Journals

eISSN - 2314-8896

pISSN - 2314-8888

DOI - 10.1155/2003/932158

Subject(s) - mathematics , bounded function , exponent , mathematical analysis , banach space , logarithm , lorentz transformation , singular integral , pure mathematics , lorentz space , variable (mathematics) , space (punctuation) , type (biology) , cauchy distribution , function (biology) , lyapunov exponent , integral equation , physics , nonlinear system , philosophy , linguistics , evolutionary biology , biology , ecology , classical mechanics , quantum mechanics

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

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