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2013 Two-weight norm inequalities for potential type and maximal operators in a metric space
Anna Kairema
Publ. Mat. 57(1): 3-56 (2013).

Abstract

We characterize two-weight norm inequalities for potential type integral operators in terms of Sawyer-type testing conditions. Our result is stated in a space of homogeneous type with no additional geometric assumptions, such as group structure or non-empty annulus property, which appeared in earlier works on the subject. One of the new ingredients in the proof is the use of a finite collection of adjacent dyadic systems recently constructed by the author and T. Hytönen. We further extend the previous Euclidean characterization of two-weight norm inequalities for fractional maximal functions into spaces of homogeneous type.

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Anna Kairema. "Two-weight norm inequalities for potential type and maximal operators in a metric space." Publ. Mat. 57 (1) 3 - 56, 2013.

Information

Published: 2013
First available in Project Euclid: 18 December 2012

zbMATH: 1284.42055
MathSciNet: MR3058926

Subjects:
Primary: 30L99, 47B38

Rights: Copyright © 2013 Universitat Autònoma de Barcelona, Departament de Matemàtiques

JOURNAL ARTICLE
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Vol.57 • No. 1 • 2013
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