Bilinear θ-type Calderón–Zygmund operators and its commutator on generalized weighted Morrey spaces over RD-spaces

Abstract

An RD-space X is a space of homogeneous type in the sense of Coifman and Weiss with the extra property that a reverse doubling property holds in X. The authors establish the boundedness of the bilinear θ-type Calderón–Zygmund operator Tθ and its commutator [b1,b2,Tθ] in this setting. These are generated by the function b1,b2∈BMO(μ) and Tθ on generalized weighted Morrey space Mp,ϕ(ω) and generalized weighted weak Morrey space WMp,ϕ(ω) over RD-spaces.

Keywords

• RD-space
• θ-type Calderón–Zygmund operator
• Commutator
• Generalized weighted Morrey spaces