Weak type estimates of commutators on Herz type spaces with variable exponent

Abstract

In this paper, first we establish the weak type $\mathrm{B}\mathrm{M}\mathrm{O}$ estimates of the commutators of the maximal operator, the fractional maximal operator and some commutators related to linear operators on the Herz type spaces with variable exponent. Subsequently the weak type Lipschitz estimates of Calderón–Zygmund singular integral commutator and fractional integral commutator from Herz-type Hardy spaces with variable exponent to weak Herz spaces with variable exponent are obtained.

Keywords:

• Weak type estimate
• $\mathrm{B}\mathrm{M}\mathrm{O}$(bounded mean oscillation)
• commutator
• Herz type spaces
• variable exponent

MR(2010)Subject Classifications:

• 42B20
• 42B35
• 46E30

Acknowledgments

The author is very grateful to the referees for their valuable comments.

Disclosure statement

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

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This work was supported by National Natural Science Foundation of China [Tianyuan Fund for Mathematics, Grant Nos. 11926343 and 11926342].