id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-2507	Menekse Yilmaz, Mine; Uysal, Gumrah	Convergence of Singular Integral Operators in Weighted Lebesgue Spaces	2017	13	.pdf	application/pdf	3964	252	79	A point x0 ∈ 〈a, b〉 is called µ−generalized Lebesgue point of the function f ∈ L1 〈a, b〉 , if lim h→0 1 µ (h) h∫ 0 |f(x0 + t)− f(x0)| dt = 0, where the function µ : R → R is increasing and absolutely continuous on [0, b− a] and µ(0) = 0 If x0 ∈ 〈a, b〉 is a common µ−generalized Lebesgue point of functions f ∈ L1,w 〈a, b〉 and w ∈ L1 〈a, b〉 , then lim (x,λ)→(x0,λ0) Lλ(f ;x) = f(x0) on any planar set Z on which the function x0+δ∫ x0−δ |Kλ(t− x)|w(t) ∣∣{µ(|x0 − t|)}′t ∣∣ dt+ 2 |Kλ (0)|w (x)µ (|x0 − x|) , 0 < δ < δ0, where δ0 is a fixed positive real number, is bounded as (x, λ) tends to (x0, λ0).	cache/ejpam-2507.pdf	txt/ejpam-2507.txt