A study on pointwise approximation by double singular integral operators
JOURNAL OF INEQUALITIES AND APPLICATIONS, vol.2015, 2015 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 2015
- Publication Date: 2015
- Doi Number: 10.1186/s13660-015-0615-6
- Journal Name: JOURNAL OF INEQUALITIES AND APPLICATIONS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Keywords: mu-generalized Lebesgue point, radial kernel, rate of convergence, bimonotonicity, bounded bivariation, CONVERGENCE
- Open Archive Collection: AVESIS Open Access Collection
- Ankara University Affiliated: Yes
Abstract
In the present work we prove the pointwise convergence and the rate of pointwise convergence for a family of singular integral operators with radial kernel in two-dimensional setting in the following form: Lx(f;x,y) = integral integral(D)f(t,s)H-lambda(t-x,s-y)dt ds, (x,y) is an element of D, where D = < a, b > x < c,d > is an arbitrary closed, semi-closed or open region in R-2 and lambda is an element of Lambda, Lambda is a set of non-negative numbers with accumulation point lambda(0). Also we provide an example to justify the theoretical results. MSC: Primary 41A35; secondary 41A25