Abstract
The main goal of this paper is to establish the boundedness of bilinear strongly singular operator (T) and its commutator (T)b1,b2 on generalized Morrey spaces Mup(μ)over non-homogeneous metric measure spaces.Under assumption that the Lebesgue measurable functions u,u1 and u2 belong to Wτ for τ ∈(0,2),and u1u2=u.The authors prove that (T) is bounded from product spaces Mu1p1(μ×Mu2p2(μ)into spaces Mup(μ),where 1/p=1/p1+1/p2 with 1＜p1,p2＜∞;and also bounded from product spaces Mu1p1(μ)×Mu2p2(μ)into generalized weak Morrey spaces WMup(μ).Furthermore,the author also show that commutator (T)b1,b2generated by b1,b2 ∈RBMO(μ)and (T) is bounded from product spaces Mu1p1(μ)× Mu2p2(μ)into spaces Mup(μ).
基金项目
国家自然科学基金(12201500)
Science Foundation for Youths of Gansu Province(22JR5RA173)
Young Teachers'Scientific Research Ability Promotion Project of Northwest Normal University(NWNU-LKQN2O20-07)
NETL
NSTL
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