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On nonlinear bivariate m 1 , m 2 − singular integral operators
Author(s) -
Uysal Gümrah
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5425
Subject(s) - mathematics , bivariate analysis , pointwise convergence , kernel (algebra) , lebesgue integration , pointwise , pure mathematics , nonlinear system , convergence (economics) , integrable system , mathematical analysis , sobolev space , discrete mathematics , approx , statistics , physics , quantum mechanics , computer science , economics , economic growth , operating system
In this paper, we give some pointwise convergence and Fatou type convergence theorems for a family of nonlinear bivariatem 1 , m 2− singular integral operators in the following form:Tωm 1 , m 2f ; x , y= ∬ R 2K ωt , s , ∑ v 1 = 1m 1∑ v 2 = 1m 2( − 1 ) ( v 1 + v 2 )m 1v 1m 2v 2f x + v 1 t , y + v 2 sd s d t ,where m 1 , m 2 ≥ 1 are fixed natural numbers,x , y ∈ R 2 and ω ∈ Ω, Ω denotes a nonempty set of indices endowed with a topology. Here,K ωω ∈ Ωdenotes a family of kernel functions and f belongs to the space of Lebesgue integrable functions LR 2. Some numerical examples and graphical illustrations supporting the results are also given.