A trace inequality for generalized potentials in Lebesgue spaces with variable exponent. Issue 1 (2004)

• Record Type: Journal Article
• Authors: Edmunds Edmunds, David E. David E.; Kokilashvili Kokilashvili, Vakhtang Vakhtang; Meskhi Meskhi, Alexander Alexander
• Other Names: Stepanov Stepanov Vladimir Vladimir Academic Editor.
• Is Part Of: Journal of function spaces and applications. Volume 2:Issue 1(2004)
• Page Start: 55
• Page End: 69
• Publication Date: 2004
• Subjects: Trace inequality, Riesz potentials, generalized Lebesgue spaces, spaces of homogeneous type.; Function spaces -- Periodicals; 515.73
• DOI: 10.1155/2004/502312
• Languages: English
• ISSNs: 0972-6802

Abstract

Abstract : A trace inequality for the generalized Riesz potentials I α ( x ) is established in spaces L p ( 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 I α ( x ) defined on fractal sets is derived.