On the boundedness of B-maximal commutators, commutators of B-Riesz potentials and B-singular integral operators in modified B-Morrey spaces

AYKOL KOCAKUŞAKLI C., Hasanov J. J.

ACTA SCIENTIARUM MATHEMATICARUM, cilt.86, sa.3-4, ss.521-547, 2020 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 86 Sayı: 3-4
  • Basım Tarihi: 2020
  • Doi Numarası: 10.14232/actasm-020-224-y
  • Dergi Adı: ACTA SCIENTIARUM MATHEMATICARUM
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.521-547
  • Anahtar Kelimeler: commutator, generalized shift operator, B-maximal function, B-Riesz potential, Morrey space, modified Morrey space, BMO gamma space, WEIGHTED NORM INEQUALITIES, SUFFICIENT CONDITIONS
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper we consider the generalized shift operator associated to the Laplace-Bessel differential operator Delta(B) and investigate B-maximal commutators, commutators of B-Riesz potentials and commutators of B-singular integral operators associated to the generalized shift operator. The boundedness of the B-maximal commutator M-b,M-gamma and the commutator [b, A(gamma)] of the B-singular integral operator on the modified B-Morrey spaces (L) over tilde (p,lambda,gamma)(R-k(n),+) for all 1 < p < infinity when b is an element of BMO gamma(R-k(n),+) are proved. In addition, we obtain that the commutator [b, I-alpha,I-gamma] of the B-Riesz potential I-alpha,I-gamma is bounded from the modified B-Morrey space (L) over tilde (p,lambda,gamma)(R-k(n),(+)) to (L) over tildeq,lambda,gamma(R-k(n),+), 1 < p < n+|gamma|-lambda/alpha, alpha/n+vertical bar gamma vertical bar <= 1/p - 1/q <= alpha/n+vertical bar gamma vertical bar - lambda and from the space (L) over tilde1, lambda, gamma (R-k(n),(+)) to W (L) over tilde (q,lambda,gamma) (R-k(n),(+)), alpha/n+vertical bar gamma vertical bar <= 1 - 1/q <= alpha/n+vertical bar gamma vertical bar - lambda.