Abstract
In this paper, we study two-weight norm inequalities for operators of potential type in homogeneous spaces. We improve some of the results given in [6] and [8] by significantly weakening their hypotheses and by enlarging the class of operators to which they apply. We also show that corresponding results of Carleson type for upper half-spaces can be derived as corollaries of those for homogeneous spaces. As an application, we obtain some necessary and sufficient conditions for a large class of weighted norm inequalities for maximal functions under various assumptions on the measures or spaces involved.
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Research of the first author was supported in part by NSERC grant A5149.
Research of the second author was supported in part by NSF grant DMS93-02991.
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Sawyer, E.T., Wheeden, R.L. & Zhao, S. Weighted norm inequalities for operators of potential type and fractional maximal functions. Potential Anal 5, 523–580 (1996). https://doi.org/10.1007/BF00275794
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DOI: https://doi.org/10.1007/BF00275794