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 ${\mathcal{G}}_{\alpha }$, $g_{\alpha }$, $g_{\tilde{\lambda },\alpha }^{\ast }$ and their commutators $[b,{\mathcal{G}}_{\alpha }]$, $[b,g_{\alpha }]$ and $[b,g_{\tilde{\lambda },\alpha }^{\ast }]$ generated with λ-central BMO functions $b\in \mathrm{CBM}{O}^{p,\lambda }\left({\mathbb{R}}^n\right)$ on generalized central Morrey spaces ${\mathcal{B}}^{q,\phi }\left({\mathbb{R}}^n\right)$ for $1<q<\mathrm{\infty },0<\alpha \le 1$, respectively. All of the results are new even on the central Morrey spaces ${\mathcal{B}}^{q,\lambda }\left({\mathbb{R}}^n\right)$.

Keywords:

• Intrinsic square functions
• commutators
• λ-central BMO functions
• generalized central Morrey spaces

AMS Subject Classifications:

• Primary: 42B20
• Secondary: 42B25

Acknowledgements

The authors would like to express their gratitude to the referee for his very valuable comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research was supported by the NNSF of China [grant number 12061069].