Two weighted inequalities forB-fractionalintegrals
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2016
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Abstract
In this paper we prove a two weighted inequality for Riesz potentialsIα,γf(B-fractional integrals) associated with the Laplace-Bessel differential operator B=∑ni=1∂2∂x2i+∑kj=1γjxj∂∂xj. This result is an analog of Heinig’s result (Indiana Univ.Math. J. 33(4):573-582,1984) for theB-fractional integral. Further, the Stein-Weissinequality forB-fractional integrals is proved as an application of this result
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Laplace-Bessel differential operator;B-fractional integrals; Stein-Weissinequality