Endpoint estimates for multilinear operators of some sublinear operators on Herz and Herz type Hardy spaces

2005 ◽  
Vol 42 (2) ◽  
pp. 131-151
Author(s):  
L. Liu
Keyword(s):  
Hardy Spaces ◽  
Integral Operators ◽  
Multilinear Operators ◽  
Marcinkiewicz Operator ◽  
Sublinear Operators

In this paper the endpoint estimates for some multilinear operators related to certain sublinear integral operators on Herz and Herz type Hardy spaces are obtained. The operators include Littlewood-Paley operator and Marcinkiewicz operator.

scholarly journals Estimates of multilinear singular integral operators and mean oscillation

2014 ◽  
Vol 95 (109) ◽  
pp. 201-214
Author(s):  
Lanzhe Liu
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Orlicz Spaces ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Multilinear Operators ◽  
Lebesgue Spaces ◽  
Marcinkiewicz Operator ◽  
Mean Oscillation

We prove the boundedness properties for some multilinear operators related to certain integral operators from Lebesgue spaces to Orlicz spaces. The operators include Calder?n-Zygmund singular integral operator, Littlewood-Paley operator and Marcinkiewicz operator.

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 Variable Anisotropic Hardy Spaces with Variable Exponents

2021 ◽  
Vol 9 (1) ◽  
pp. 65-89
Author(s):  
Zhenzhen Yang ◽  
Yajuan Yang ◽  
Jiawei Sun ◽  
Baode Li
Keyword(s):  
Hardy Spaces ◽  
Variable Exponent ◽  
Atomic Decomposition ◽  
Integral Operators ◽  
Moment Condition ◽  
Variable Exponents ◽  
Hölder Continuous ◽  
Multi Level ◽  
The Moment ◽  
Variable Anisotropy

Abstract Let p(·) : ℝ n → (0, ∞] be a variable exponent function satisfying the globally log-Hölder continuous and let Θ be a continuous multi-level ellipsoid cover of ℝ n introduced by Dekel et al. [12]. In this article, we introduce highly geometric Hardy spaces Hp (·)(Θ) via the radial grand maximal function and then obtain its atomic decomposition, which generalizes that of Hardy spaces Hp (Θ) on ℝ n with pointwise variable anisotropy of Dekel et al. [16] and variable anisotropic Hardy spaces of Liu et al. [24]. As an application, we establish the boundedness of variable anisotropic singular integral operators from Hp (·)(Θ) to Lp (·)(ℝ n ) in general and from Hp (·)(Θ) to itself under the moment condition, which generalizes the previous work of Bownik et al. [6] on Hp (Θ).

Boundedness of multi-parameter pseudo-differential operators on multi-parameter local Hardy spaces

2020 ◽  
Vol 32 (4) ◽  
pp. 919-936 ◽  
Author(s):  
Jiao Chen ◽  
Wei Ding ◽  
Guozhen Lu
Keyword(s):  
Hardy Spaces ◽  
Differential Operators ◽  
Integral Operators ◽  
Fourier Multipliers ◽  
Regularity Of Solutions ◽  
Local Version ◽  
Fourier Integral Operators ◽  
Pseudo Differential Operators ◽  
Local Hardy Spaces ◽  
The One

AbstractAfter the celebrated work of L. Hörmander on the one-parameter pseudo-differential operators, the applications of pseudo-differential operators have played an important role in partial differential equations, geometric analysis, harmonic analysis, theory of several complex variables and other branches of modern analysis. For instance, they are used to construct parametrices and establish the regularity of solutions to PDEs such as the {\overline{\partial}} problem. The study of Fourier multipliers, pseudo-differential operators and Fourier integral operators has stimulated further such applications. It is well known that the one-parameter pseudo-differential operators are {L^{p}({\mathbb{R}^{n}})} bounded for {1<p<\infty}, but only bounded on local Hardy spaces {h^{p}({\mathbb{R}^{n}})} introduced by Goldberg in [D. Goldberg, A local version of real Hardy spaces, Duke Math. J. 46 1979, 1, 27–42] for {0<p\leq 1}. Though much work has been done on the {L^{p}(\mathbb{R}^{n_{1}}\times\mathbb{R}^{n_{2}})} boundedness for {1<p<\infty} and Hardy {H^{p}(\mathbb{R}^{n_{1}}\times\mathbb{R}^{n_{2}})} boundedness for {0<p\leq 1} for multi-parameter Fourier multipliers and singular integral operators, not much has been done yet for the boundedness of multi-parameter pseudo-differential operators in the range of {0<p\leq 1}. The main purpose of this paper is to establish the boundedness of multi-parameter pseudo-differential operators on multi-parameter local Hardy spaces {h^{p}(\mathbb{R}^{n_{1}}\times\mathbb{R}^{n_{2}})} for {0<p\leq 1} recently introduced by Ding, Lu and Zhu in [W. Ding, G. Lu and Y. Zhu, Multi-parameter local Hardy spaces, Nonlinear Anal. 184 2019, 352–380].

Boundedness for Multilinear Singular Integral Operators on Some Hardy and Herz Type Spaces

2005 ◽  
Vol 12 (2) ◽  
pp. 309-320
Author(s):  
Lanzhe Liu
Keyword(s):  
Singular Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Lipschitz Functions ◽  
Multilinear Operators ◽  
Multilinear Singular Integral ◽  
Type Spaces

Abstract In this paper, we prove the boundedness for some multilinear operators generated by singular integral operators and Lipschitz functions on some Hardy and Herz type spaces.

Oscillatory singular integral operators with Hölder class kernels on Hardy spaces

2019 ◽  
Vol 31 (2) ◽  
pp. 535-542
Author(s):  
Yibiao Pan
Keyword(s):  
Singular Integral ◽  
Hardy Spaces ◽  
Singular Integrals ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Oscillatory Singular Integral ◽  
Hölder Class ◽  
Holder Class ◽  
Oscillatory Singular Integrals

AbstractA sharp logarithmic bound is established for the {H^{1}}-norm of oscillatory singular integrals with quadratic phases and Hölder class kernels. Prior results had relied on a {C^{1}}-assumption on the kernel.

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

Sign in / Sign up

Export Citation Format

Share Document