SOME THEOREMS ON THE APPROXIMATION OF NON-INTEGRABLE FUNCTIONS VIA SINGULAR INTEGRAL OPERATORS
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In this paper we study the pointwise approximation of func- tions which are non-integrable on D =< -π, π > × < -π, π > where <-π,π> × <-π,π> is a closed, semi-closed or open region, by double singular integral operators with radial kernels of the form: Lλ (f; x, y) = ∫ D f (s, t)Kλ (√(s - x)2 + (t - y)2)) dsdt at generalized Lebesgue point. Also we investigate the rate of conver- gence of the operators Lλ (f, x, y) at this point.
Abstract
In this paper we study the pointwise approximation of func- tions which are non-integrable on D =< -π, π > × < -π, π > where <-π,π> × <-π,π> is a closed, semi-closed or open region, by double singular integral operators with radial kernels of the form: Lλ (f; x, y) = ∫ D f (s, t)Kλ (√(s - x)2 + (t - y)2)) dsdt at generalized Lebesgue point. Also we investigate the rate of conver- gence of the operators Lλ (f, x, y) at this point.
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