Boundedness of intrinsic square functions and commutators on generalized central Morrey spaces

Abstract

In this paper, the authors establish the boundedness for a large class of intrinsic square functions G α , g α , g λ ~ , α ∗ and their commutators [ b , G α ] , [ b , g α ] and [ b , g λ ~ , α ∗ ] generated with λ-central BMO functions b ∈ CBM O p , λ ( R n ) on generalized central Morrey spaces B q , φ ( R n ) for 1 < q < ∞ , 0 < α ≤ 1 , respectively. All of the results are new even on the central Morrey spaces B q , λ ( R n ) .