WEIGHTED BOUNDEDNESS OF THE FRACTIONAL MAXIMAL OPERATOR AND RIESZ POTENTIAL GENERATED BY GEGENBAUER DIFFERENTIAL OPERATOR

Ibrahimov E. J., Guliyev V. S., Jafarova S. A.

TRANSACTIONS OF A RAZMADZE MATHEMATICAL INSTITUTE, vol.173, no.3, pp.45-78, 2019 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 173 Issue: 3
  • Publication Date: 2019
  • Journal Name: TRANSACTIONS OF A RAZMADZE MATHEMATICAL INSTITUTE
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.45-78
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

In the paper we study the weighted (L-p,(omega),(lambda), L-q,L-omega,L-lambda)-boundedness of the fractional maximal operator Mb' (G is a fractional maximal operator) and the Riesz potential (G is the Riesz potential) generated by the Gegenbauer differential operator G(lambda ) G = (x(2) - 1)(1/2-lambda )d/dx (x(2) - 1)(lambda+1/2 )d/dx, x is an element of (1,infinity), lambda is an element of (0,1/2).