Riesz fractional integrals in grand lebesgue spaces on ℝn

Samko, Stefan; Umarkhadzhiev, Salaudin

http://hdl.handle.net/10400.1/9446

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Authors

Samko, Stefan

Umarkhadzhiev, Salaudin

Abstract(s)

We introduce conditions on the construction of grand Lebesgue spaces on R-n which imply the validity of the Sobolev theorem for the Riesz fractional integrals I-alpha and the boundedness of the maximal operator, in such spaces. We also give an inversion of the operator I-alpha by means of hypersingular integrals, within the frameworks of the introduced spaces. We also proof the denseness of C-0(infinity)(R-n) in a subspace of the considered grand space.