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Boundary Regularity for Harmonic Hardy–Sobolev Spaces
Author(s) -
Beatrous F.,
Burbea J.
Publication year - 1989
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-39.1.160
Subject(s) - mathematics , bounded mean oscillation , hardy space , lipschitz continuity , sobolev space , bounded function , harmonic function , mathematical analysis , boundary (topology) , embedding , interpolation space , harmonic measure , pure mathematics , maximal function , oscillation (cell signaling) , harmonic , functional analysis , physics , quantum mechanics , biochemistry , chemistry , genetics , artificial intelligence , biology , computer science , gene
Two scales of harmonic Hardy‐Sobolev spaces are introduced and their boundary regularity is studied. Both scales impose conditions on derivatives of harmonic functions in a fixed direction. In one case, they are required to have bounded P ‐means, while in the other, they are required to have non‐tangentialmaximal functions in L p . The results include embedding in Lipschitz spaces, as well as into spaces of continuous functions and spaces of bounded and vanishing mean oscillation. In particular, real variable versions of the theorem of Privalov on analytic functions with absolutely continuous boundary values are proved.