Estimate for some integral operators and their commutators on generalized fractional mixed Morrey spaces

In this paper, we first establish the definition of a generalized fractional mixed Morrey space Lp,.,.(Rn), where p=( p1, p2, center dot center dot center dot, pn), 1 < p=8 and. :(0, 8).(0, 8) is an increasing function satisfying certain doubling conditions. Second, we prove that the Calderon-Zygmund integral operator Tand its commutator [ b, T] which is generated by Tand b. BMO(Rn) are bounded from spaces Lp,.,.(Rn) into spaces Lp,.,.(Rn); furthermore, we prove that the fractional integral operator Iaand its commutator [ b, Ia] formed by b. BMO(Rn) and Iaare bounded from the spaces Lp,.,.(Rn) into spaces Lq,.- a,.(Rn), where 1 < p< q<8, n j=11qj= n j=11pj- aand n j=11pj=.> a > 0. Finally, the boundedness for the fractional maximal operator Ma, the commutator [ b, Ma] associated with BMOfunctions and the commutator [ b, T] formed by Tand b. Lip ss(Rn) on spaces Lp,.,.(Rn) is established, respectively. (c) 2023 Elsevier Masson SAS. All rights reserved.