Open AccessOn the rate of $L_p$-convergence of Balakrishnan--Rubin-type hypersingular integrals associated to the Gauss-Weierstrass semigroup
Author(s) -
Melih Eryiğit,
Selim Çobanoğlu
Publication year - 2017
Publication title -
turkish journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.454
H-Index - 27
eISSN - 1303-6149
pISSN - 1300-0098
DOI - 10.3906/mat-1610-105
Subject(s) - mathematics , semigroup , gauss , smoothness , order (exchange) , type (biology) , rate of convergence , mathematical analysis , pure mathematics , combinatorics , key (lock) , ecology , physics , finance , quantum mechanics , economics , biology
We introduce a family of Balakrishnan–Rubin-type hypersingular integrals depending on a parameter ε and generated by the Gauss–Weierstrass semigroup. Then the connection between the order of Lp –smoothness of a Lp –function φ and the rate of Lp -convergence of these families to φ , as ε tends to 0, is obtained.
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