On Sobolev Theorem for Riesz-Type Potentials in Lebesgue Spaces with Variable Exponent | Zendy

Vakhtang Kokilashvili | Zendy; Stefan Samko | Zendy

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On Sobolev Theorem for Riesz-Type Potentials in Lebesgue Spaces with Variable Exponent

Author(s) -

Vakhtang Kokilashvili,

Stefan Samko

Publication year - 2003

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1178

Subject(s) - mathematics , sobolev space , riesz potential , lp space , lebesgue's number lemma , exponent , type (biology) , pure mathematics , lebesgue integration , standard probability space , mathematical analysis , banach space , riemann integral , operator theory , ecology , linguistics , philosophy , biology , fourier integral operator

The Riesz potential operator of variable order fi(x) is shown to be bounded from the Lebesgue space Lp(¢)(Rn) with variable exponent p(x) into the weighted space L q(¢) ‰ (R n ), where ‰ = (1 + jxj)¡∞ with some ∞ > 0 and 1 q(x) = 1 p(x) ¡ fi(x) n when p(x) is not necessarily constant at inflnity. It is as- sumed that the exponent p(x) satisfles the logarithmic continuity condition both locally and at inflnity and 1 < p(1) • p(x) • P < 1; x 2Rn.

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