A GENERALIZATION OF PARABOLIC RIESZ AND PARABOLIC BESSEL POTENTIALS

Aliev I. A., SEKİN Ç.

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, vol.50, no.3, pp.815-824, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 50 Issue: 3
  • Publication Date: 2020
  • Doi Number: 10.1216/rmj.2020.50.815
  • Journal Name: ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.815-824
  • Keywords: parabolic potentials, Gauss-Weierstrass kernel, integral operators, WAVELET TRANSFORMS, LEBESGUE SPACES
  • Akdeniz University Affiliated: Yes

Abstract

Classical parabolic Riesz and parabolic Bessel type potentials are interpreted as negative fractional powers of the differential operators (-Delta + partial derivative/partial derivative t) and (I - Delta+ partial derivative/partial derivative t). Here, Delta is the Laplacian and I is the identity operator. We introduce some generalizations of these potentials, namely, we define the family of operators A(beta,theta)(alpha) = (theta I + (-Delta)(beta/2) + partial derivative/partial derivative t)(-alpha) for theta >= 0 and alpha, beta > 0, and investigate its behavior in the framework of L-p (Rn+1)-spaces.