Boundedness criteria for singular integrals in weighted grand lebesgue spaces

Author: Kokilashvili V.  

Publisher: Springer Publishing Company

ISSN: 1072-3374

Source: Journal of Mathematical Sciences, Vol.170, Iss.1, 2010-10, pp. : 20-33

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Abstract

Boundedness criteria for the Calderón singular integral, Riesz transform and Cauchy singular integral in generalized weighted grand Lebesgue spaces L p),θ w , 1 < p < ∞, are studied. It is shown that an operator K of this type is bounded in L p),θ w if and only if the weight w satisfies the Muckenhoupt A p condition. Bibliography: 15 titles.