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Trace Inequalities of Sobolev Type in the Upper Triangle Case
Author(s) -
Cascante Carme,
Ortega Joaquín M.,
Verbitsky Igor E.
Publication year - 2000
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611500012260
Subject(s) - mathematics , unit sphere , trace (psycholinguistics) , mathematics subject classification , holomorphic function , pure mathematics , sobolev space , type (biology) , sobolev inequality , ball (mathematics) , characterization (materials science) , isotropy , combinatorics , mathematical analysis , physics , philosophy , linguistics , ecology , quantum mechanics , optics , biology
We give a new non‐capacitary characterization of positive Borel measures μ on R n such that the potential space I α* L p is imbedded in L q ( d μ) for $1∪ q ∪ p ∪+∞, that is, the trace inequality ∥ I α f ∥ L q ( d μ ) ⩽ C ∥ f ∥ L p ( d x )holds, for Riesz potentials I α = (‐ Δ) α2 . A weak‐type trace inequality is also characterized. A non‐isotropic version on the unit sphere S n is studied, as well as the holomorphic case for Hardy–Sobolev spaces H α p in the ball. 1991 Mathematics Subject Classification : primary 31C15, 42B20; secondary 32A35.