Nonlinear m-singular integral operators in the framework of fatou type weighted convergenc

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Tarih

2018

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Erişim Hakkı

info:eu-repo/semantics/openAccess

Özet

In the present paper, we prove some theorems concerning Fatou type weighted pointwise convergence of nonlinear msingular integral operators of the form: T [m] (f; x) = Z R K t;Xm k=1 (1)k1 m k f(x + kt) ! dt; where x 2 R; m 1 is a Önite natural number and 2 which is a nonempty set of non-negative indices, at a common m p Lebesgue point of f 2 Lp;'(R) (1 p < 1) and ': Here, ' : R ! R+ is a weight function endowed with some speciÖc properties and Lp;'(R) is the space of all measurable functions for which rable functions for which f ' p is integrabl on R.

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Kaynak

Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics

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Cilt

67

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1

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