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In this paper, we present some general results on the pointwise convergence of the non-convolution type nonlinear singular integral operators in the following form: \begin{equation*} T_{\lambda }(f;x)=\underset{\Omega }{\int }K_{\lambda }\left( t,x,f\left(t\right) \right) dt,\text{ }x\in \Psi ,\text{ }\lambda \in \Lambda , \end{equation*} where $\Psi =\left \langle a,b\right \rangle $ and $\Omega =\left \langle A,B\right \rangle $ stand for arbitrary closed, semi-closed or open bounded intervals in $\mathbb{R}$ or these set notations denote $\mathbb{R} $, and $\Lambda $ is a set of non-negative numbers, to the function $f\in L_{p,w}\left( \Omega \right) $, where $L_{p,w}\left( \Omega \right) $ denotes the space of all measurable functions $f$ for which $\left \vert \frac{f}{w}\right \vert ^{p}$ $(1\leq p<\infty )$ is integrable on $\Omega ,$ and $w: \mathbb{R} \rightarrow \mathbb{R}^{+}$ is a weight function satisfying some conditions.
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참고문헌 (28)
참고문헌 신청
G. Alexits / 1960 / Konvergenzprobleme der Orthogonalreihen / Verlag der Un-garischen Akademie der Wissenschaften
C. Bardaro / 1984 / On approximation properties for some classes of linear operators of convolution type / Atti Sem. Mat. Fis. Univ. Modena 33(2):329~356
C. Bardaro / 1990 / On approximation properties of certain noncon-volution integral operators / J. Approx. Theory 62(3):358~371
C. Bardaro / 1996 / Approximation by nonlinear integral operators in some modular function spaces / Ann. Polon. Math 63:173~182
C. Bardaro / 2003 / Nonlinear integral operators and applications / Walter de Gruyter, Publ
C. Bardaro / 1984 / On approximation properties for some classes of linear operators of convolution type / Atti Sem. Mat. Fis. Univ. Modena 33(2):329~356
C. Bardaro / 1990 / On approximation properties of certain noncon-volution integral operators / J. Approx. Theory 62(3):358~371
C. Bardaro / 1996 / Approximation by nonlinear integral operators in some modular function spaces / Ann. Polon. Math 63:173~182
C. Bardaro / 2003 / Nonlinear integral operators and applications / Walter de Gruyter, Publ
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