A GENERALIZATION OF PARABOLIC RIESZ AND PARABOLIC BESSEL POTENTIALS

Aliev I. A., SEKİN Ç.

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, cilt.50, sa.3, ss.815-824, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 50 Sayı: 3
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1216/rmj.2020.50.815
  • Dergi Adı: ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.815-824
  • Anahtar Kelimeler: parabolic potentials, Gauss-Weierstrass kernel, integral operators, WAVELET TRANSFORMS, LEBESGUE SPACES
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.