BMO harmonic approximation in the plane and spectral synthesis for Hardy-Sobolev spaces.

Mateu, Joan, and Verdera Melenchón, Joan. "BMO harmonic approximation in the plane and spectral synthesis for Hardy-Sobolev spaces.." Revista Matemática Iberoamericana 4.2 (1988): 291-318. <http://eudml.org/doc/39375>.

@article{Mateu1988,
abstract = {The spectral synthesis theorem for Sobolev spaces of Hedberg and Wolff [7] has been applied in combination with duality, to problems of Lq approximation by analytic and harmonic functions. In fact, such applications were one of the main motivations to consider spectral synthesis problems in the Sobolev space setting. In this paper we go the opposite way in the context of the BMO-H1 duality: we prove a BMO approximation theorem by harmonic functions and then we apply the ideas in its proof to produce a spectral synthesis result for variants of Sobolev spaces involving the Fefferman-Stein Hardy space H1.},
author = {Mateu, Joan, Verdera Melenchón, Joan},
journal = {Revista Matemática Iberoamericana},
keywords = {Funciones de oscilación media acotada; Espacios de Hardy; Espacios de Sobolev; Análisis funcional; Bidimensionalidad; Síntesis; Función armónica; BMO harmonic approximation; Hardy-Sobolev spaces},
language = {eng},
number = {2},
pages = {291-318},
title = {BMO harmonic approximation in the plane and spectral synthesis for Hardy-Sobolev spaces.},
url = {http://eudml.org/doc/39375},
volume = {4},
year = {1988},
}

TY - JOUR
AU - Mateu, Joan
AU - Verdera Melenchón, Joan
TI - BMO harmonic approximation in the plane and spectral synthesis for Hardy-Sobolev spaces.
JO - Revista Matemática Iberoamericana
PY - 1988
VL - 4
IS - 2
SP - 291
EP - 318
AB - The spectral synthesis theorem for Sobolev spaces of Hedberg and Wolff [7] has been applied in combination with duality, to problems of Lq approximation by analytic and harmonic functions. In fact, such applications were one of the main motivations to consider spectral synthesis problems in the Sobolev space setting. In this paper we go the opposite way in the context of the BMO-H1 duality: we prove a BMO approximation theorem by harmonic functions and then we apply the ideas in its proof to produce a spectral synthesis result for variants of Sobolev spaces involving the Fefferman-Stein Hardy space H1.
LA - eng
KW - Funciones de oscilación media acotada; Espacios de Hardy; Espacios de Sobolev; Análisis funcional; Bidimensionalidad; Síntesis; Función armónica; BMO harmonic approximation; Hardy-Sobolev spaces
UR - http://eudml.org/doc/39375
ER -