Littlewood-Paley $g^{\ast}_{\lambda,\mu}$-function and Its Commutator on Non-homogeneous Generalized Morrey Spaces

The aim of this paper is to establish the boundednes of the commutator $[b,T_{\alpha }]$ [ b , T α ] generated by θ-type generalized fractional integral $T_{\alpha }$ T α and $b\in \widetilde{\mathrm{RBMO}}(\mu )$ b ∈ RBMO ˜ ( μ ) over a non-homogeneous metric measure space. Under the assumption that the dominating function λ satisfies the ϵ-weak reverse doubling condition, the author proves that the commutator $[b,T_{\alpha }]$ [ b , T α ] is bounded from the Lebesgue space $L^{p}(\mu )$ L p ( μ ) into the space $L^{q}(\mu )$ L q ( μ ) for $\frac{1}{q}=\frac{1}{p}-\alpha $ 1 q = 1 p − α and $\alpha \in (0,1)$ α ∈ ( 0 , 1 ) , and bounded from the atomic Hardy space $\widetilde{H}^{1}_{b}(\mu )$ H ˜ b 1 ( μ ) with discrete coefficient into the space $L^{\frac{1}{1-\alpha },\infty }(\mu )$ L 1 1 − α , ∞ ( μ ) . Furthermore, the boundedness of the commutator $[b,T_{\alpha }]$ [ b , T α ] on a generalized Morrey space and a Morrey space is also got.

show abstract

Boundedness of some operators on grand generalized Morrey spaces over non-homogeneous spaces

He¹,

Tao²

2021

MATH

View full text Add to dashboard Cite

<abstract><p>The aim of this paper is to obtain the boundedness of some operator on grand generalized Morrey space $ \mathcal{L}^{p), \varphi, \phi}_{\mu}(G) $ over non-homogeneous spaces, where $ G\subset $ $ \mathbb{R}^{n} $ is a bounded domain. Under assumption that functions $ \varphi $ and $ \phi $ satisfy certain conditions, the authors prove that the Hardy-Littlewood maximal operator, fractional integral operators and $ \theta $-type Calderón-Zygmund operators are bounded on the non-homogeneous grand generalized Morrey space $ \mathcal{L}^{p), \varphi, \phi}_{\mu}(G) $. Moreover, the boundedness of commutator $ [b, T^{G}_{\theta}] $ which is generated by $ \theta $-type Calderón-Zygmund operator $ T_{\theta} $ and $ b\in\mathrm{RBMO}(\mu) $ on spaces $ \mathcal{L}^{p), \varphi, \phi}_{\mu}(G) $ is also established.</p></abstract>

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

hi@scite.ai

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Littlewood-Paley $g^{\ast}_{\lambda,\mu}$-function and Its Commutator on Non-homogeneous Generalized Morrey Spaces

Cited by 3 publications

References 13 publications

Bilinear $$\theta $$-type Calderón–Zygmund operator and its commutator on non-homogeneous weighted Morrey spaces

Bilinear $$\theta $$-type Calderón–Zygmund operator and its commutator on non-homogeneous weighted Morrey spaces

Commutators of θ-type generalized fractional integrals on non-homogeneous spaces

Boundedness of some operators on grand generalized Morrey spaces over non-homogeneous spaces

Contact Info

Product

Resources

About