Generalized Homogeneous Littlewood–Paley g-Function on Some Function Spaces

Lü, Guanghui; Tao, Shuangping

doi:10.1007/s40840-020-00934-7

Cited by 7 publications

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References 27 publications

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“…In 2017, Lin et al [16] proved that the commutator T b , which is generated by Calderón-Zygmund operator T and b ∈ RBMO(μ), is bounded from space H 1 (μ) to space L 1,∞ (μ), and also bounded on space L p (μ) for all p ∈ (1, ∞). For more progresses on the properties of function spaces and the boundedness of operators on (X , d, μ), we can see [2], [4], [7], [15], [17]- [21] and so on.…”

Section: §1 Introductionmentioning

confidence: 99%

Fractional Type Marcinkiewicz Integral and Its Commutator on Nonhomogeneous Spaces

Lü¹

2022

Nagoya Math. J.

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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.

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