Revista Matemática Complutense

, Volume 23, Issue 2, pp 355–381 | Cite as

Singular and fractional integral operators on Campanato spaces with variable growth conditions

Article

Abstract

Let X be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, we prove boundedness of singular and fractional integral operators on Campanato spaces over X with variable growth conditions. The function spaces contain generalized Lipschitz spaces with variable exponent as special cases. Moreover, by using the function spaces, we can deal with functions which are Lp-functions locally on one subset in X, BMO-functions locally on one another subset and Lipα-functions locally on the other one. Our results are new even for ℝn case.

Singular integral Fractional integral Riesz potential Variable exponent Campanato space Lipschitz spaces Bounded mean oscillation Space of homogeneous type 

Mathematics Subject Classification (2000)

42B35 42B20 26A33 46E15 46E30 

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Copyright information

© Revista Matemática Complutense 2009

Authors and Affiliations

  1. 1.Department of MathematicsOsaka Kyoiku UniversityKashiwaraJapan

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