On Approximation Properties of Multivariate Class of Nonlinear Singular Integral Operators

Gumrah Uysal, Vishnu Narayan Mishra, Ertan Ibikli

Abstract


In the present paper, we study the pointwise approximation of
nonlinear multivariate singular integral operators having convolution type ker-
nels of the form:
T (f; x) =
Z
D
K (t ô€€€ x; f(t)) dt; x 2 D; 2 ;
where D =
n
i=1 hai; bii is open, semi-open or closed multidimensional arbitrary
bounded box in Rn or D = Rn and is non-empty the set of non-negative
indices, at a -generalized Lebesgue point of f 2 Lp(D): Also, we investigate
the corresponding rates of convergences at this point.


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