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

TL;DR

This paper proves the boundedness of various intrinsic square functions and their commutators with BMO functions on generalized central Morrey spaces, extending known results even in classical central Morrey spaces.

Contribution

It establishes new boundedness results for intrinsic square functions and their commutators on generalized central Morrey spaces, including cases previously unaddressed.

Findings

Boundedness of intrinsic square functions on generalized central Morrey spaces.

Boundedness of commutators with BMO functions on these spaces.

Results are novel even for classical central Morrey spaces.

Abstract

In this paper, the authors establish the boundedness for a large class of intrinsic square functions $\mathcal{G}_{\alpha}$, $g_{\alpha}$, $g^{\ast}_{\tilde{\lambda},\alpha}$ and their commutators $[b,\mathcal{G}_{\alpha}]$, $[b,g_{\alpha}]$ and $[b,g^{\ast}_{\tilde{\lambda},\alpha}]$ generated with $\lambda$-central $BMO$ functions $b\in CBMO^{p,\lambda}(\mathbb{R}^{n})$ on generalized central Morrey spaces $\mathcal{B}^{q,\varphi}(\mathbb{R}^{n})$ for $1<q<\infty,0<\alpha\leq1$, respectively. All of the results are new even on the central Morrey spaces $\mathcal{B}^{q,\lambda}(\mathbb{R}^{n})$.