scholarly journals Boundedness of Fractional Integral Operators in Weighted Weak Hardy Spaces on Homogeneous Spaces

2019 ◽  
Author(s):  
Wen-guo JIANG
Keyword(s):  
Hardy Spaces ◽  
Fractional Integral ◽  
Homogeneous Spaces ◽  
Integral Operators ◽  
Fractional Integral Operators

Fractional Integral on Martingale Hardy Spaces With Variable Exponents

2015 ◽  
Vol 18 (5) ◽  
Author(s):  
Zhiwei Hao ◽  
Yong Jiao
Keyword(s):  
Hardy Spaces ◽  
Probability Space ◽  
Fractional Integral ◽  
Integral Operators ◽  
Variable Exponents ◽  
Fractional Integral Operators

AbstractIn this paper we investigate the boundedness of fractional integral operators on predictable martingale Hardy spaces with variable exponents defined on a probability space. More precisely, let f = (f

scholarly journals Hardy spaces estimates for multilinear operators with homogeneous kernels

2003 ◽  
Vol 170 ◽  
pp. 117-133 ◽  
Author(s):  
Yong Ding ◽  
Shanzhen Lu
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Fractional Integral ◽  
Integral Operators ◽  
Kernel Functions ◽  
Multilinear Operators ◽  
Product Spaces ◽  
Bounded Operators ◽  
Fractional Integral Operators ◽  
Bmo Function

AbstractIn this paper the authors prove that a class of multilinear operators formed by the singular integral or fractional integral operators with homogeneous kernels are bounded operators from the product spaces Lp1 × Lp2 × · · · × LpK (ℝn) to the Hardy spaces Hq (ℝn) and the weak Hardy space Hq,∞(ℝn), where the kernel functions Ωij satisfy only the Ls-Dini conditions. As an application of this result, we obtain the (Lp, Lq) boundedness for a class of commutator of the fractional integral with homogeneous kernels and BMO function.

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

2021 ◽  
Vol 7 (1) ◽  
pp. 1000-1014
Author(s):  
Suixin He ◽  
◽  
Shuangping Tao
Keyword(s):  
Bounded Domain ◽  
Maximal Operator ◽  
Fractional Integral ◽  
Morrey Space ◽  
Homogeneous Spaces ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Generalized Morrey Space ◽  
Fractional Integral Operators ◽  
Littlewood Maximal Operator

<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>

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