Weighted two-parameter Bergman space inequalities
Wilson, J. Michael (University of Vermont. Department of Mathematics and Statistics)

Date:	2003
Abstract:	For f , a function defined on Rd1 ×Rd2 , take u to be its biharmonic extension into R+ +1 × Rd2 +1 . In this paper we prove strong d1 + sufficient conditions on measures µ and weights v such that the inequality 1/q q ∇2 u dµ(x1 , x2 , y1 , y2 ) d +1 d +1 R+1 ×R+2 1/p ≤ f p v dx Rd1 ×Rd2 will hold for all f in a reasonable test class, for 1 < p ≤ 2 ≤ q < ∞. Our result generalizes earlier work by R. L. Wheeden and the author on one-parameter harmonic extensions. We also obtain sufficient conditions for analogues of (∗) to hold when the entries of ∇1 ∇2 u are replaced by more general convolutions.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Bergman spaces ; Weighted norm inequalities ; Littlewood-Paley theory
Published in:	Publicacions matemàtiques, V. 47 N. 1 (2003) , p. 161-193, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/38071
DOI: 10.5565/PUBLMAT_47103_08

33 p, 276.3 KB

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