Boundedness of the Vector-Valued Intrinsic Square Functions on Variable Exponents Herz Spaces

Abstract

In this article, the authors study the boundedness of the vector-valued inequality for the intrinsic square function and the boundedness of the scalar-valued intrinsic square function on variable exponents Herz spaces K˙ρ(·)α,q(·)(Rn). In addition, the boundedness of commutators generated by the scalar-valued intrinsic square function and BMO class is also studied on K˙ρ(·)α,q(·)(Rn).

Keywords

• intrinsic square function
• vector-valued inequality
• Herz spaces
• BMO function
• variable exponent
• sublinear operators