A trace inequality for generalized potentials in Lebesgue spaces with variable exponent | Zendy

David E. Edmunds | Zendy; Vakhtang Kokilashvili | Zendy; Alexander Meskhi | Zendy

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A trace inequality for generalized potentials in Lebesgue spaces with variable exponent

Author(s) -

David E. Edmunds,

Vakhtang Kokilashvili,

Alexander Meskhi

Publication year - 2004

Publication title -

journal of function spaces

Language(s) - English

Resource type - Journals

eISSN - 2314-8896

pISSN - 2314-8888

DOI - 10.1155/2004/502312

Subject(s) - mathematics , trace (psycholinguistics) , lp space , pure mathematics , lebesgue's number lemma , standard probability space , exponent , inequality , variable (mathematics) , lebesgue integration , mathematical analysis , banach space , riemann integral , philosophy , linguistics , operator theory , fourier integral operator

A trace inequality for the generalized Riesz potentials Iα(x) is established in spaces Lp(x) defined on spaces of homogeneous type. The results are new even in the case of Euclidean spaces. As a corollary a criterion for a two-weighted inequality in classical Lebesgue spaces for potentials Iα(x) defined on fractal sets is derived

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