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Boundedness on inhomogeneous Lipschitz spaces of fractional integrals singular integrals and hypersingular integrals associated to non-doubling measures

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Abstract

In the context of a finite measure metric space whose measure satisfies a growth condition, we prove “T1” type necessary and sufficient conditions for the boundedness of fractional integrals, singular integrals, and hypersingular integrals on inhomogeneous Lipschitz spaces. We also indicate how the results can be extended to the case of infinite measure. Finally we show applications to Real and Complex Analysis.

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Authors and Affiliations

  1. Department of Mathematical Sciences, DePaul University, 2320 North Kenmore Avenue, 606143250, Chicago, Illinois, USA

    A. Eduardo Gatto

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  1. A. Eduardo Gatto
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Correspondence to A. Eduardo Gatto.

Additional information

This paper was supported by a sabbatical leave from DePaul University and by a grant from the Ministerio de Educacion y Ciencia of Spain, Ref. # SAB2006-0118 for a quarter sabbatical visit to the Centre de Recerca Matemàtica in Barcelona.

The author wants to express a deep gratitude to these institutions, to the Analysis group of the Universidad Autónoma de Barcelona, in particular to Xavier Tolsa for the invitation and to the director and staff of the CRM for their pleasant hospitality and excellent resources.

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Gatto, A.E. Boundedness on inhomogeneous Lipschitz spaces of fractional integrals singular integrals and hypersingular integrals associated to non-doubling measures. Collect. Math. 60, 101–114 (2009). https://doi.org/10.1007/BF03191219

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  • DOI: https://doi.org/10.1007/BF03191219

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