Article contents
FRACTIONAL TYPE MARCINKIEWICZ INTEGRAL AND ITS COMMUTATOR ON NONHOMOGENEOUS SPACES
Published online by Cambridge University Press: 03 June 2022
Abstract
The aim of this paper is to establish the boundedness of fractional type Marcinkiewicz integral $\mathcal {M}_{\iota ,\rho ,m}$ and its commutator $\mathcal {M}_{\iota ,\rho ,m,b}$ on generalized Morrey spaces and on Morrey spaces over nonhomogeneous metric measure spaces which satisfy the upper doubling and geometrically doubling conditions. Under the assumption that the dominating function $\lambda $ satisfies $\epsilon $ -weak reverse doubling condition, the author proves that $\mathcal {M}_{\iota ,\rho ,m}$ is bounded on generalized Morrey space $L^{p,\phi }(\mu )$ and on Morrey space $M^{p}_{q}(\mu )$ . Furthermore, the boundedness of the commutator $\mathcal {M}_{\iota ,\rho ,m,b}$ generated by $\mathcal {M}_{\iota ,\rho ,m}$ and regularized $\mathrm {BMO}$ space with discrete coefficient (= $\widetilde {\mathrm {RBMO}}(\mu )$ ) on space $L^{p,\phi }(\mu )$ and on space $M^{p}_{q}(\mu )$ is also obtained.
MSC classification
- Type
- Article
- Information
- Copyright
- © (2022) The Authors. The publishing rights in this article are licenced to Foundation Nagoya Mathematical Journal under an exclusive license
Footnotes
This work is supported by the Young Teachers’ Scientific Research Ability Promotion Project of Northwest Normal University (NWNU-LKQN2020-07) and Innovation Fund Project for Higher Education of Gansu Province (2020A-010).
References
- 5
- Cited by