scholarly journals The Boundedness of Some Integral Operators on Weighted Hardy Spaces Associated with Schrödinger Operators

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Hua Wang
Keyword(s):  
Integral Operator ◽  
Hardy Spaces ◽  
Fractional Integral ◽  
Atomic Decomposition ◽  
Integrable Function ◽  
Integral Operators ◽  
Weighted Hardy Spaces ◽  
Imaginary Power ◽  
Locally Integrable Function

LetL=-Δ+Vbe a Schrödinger operator acting onL2(Rn),n≥1, whereV≢0is a nonnegative locally integrable function onRn. In this paper, we will first define molecules for weighted Hardy spacesHLp(w)  (0<p≤1)associated withLand establish their molecular characterizations. Then, by using the atomic decomposition and molecular characterization ofHLp(w), we will show that the imaginary powerLiγis bounded onHLp(w)forn/(n+1)<p≤1, and the fractional integral operatorL-α/2is bounded fromHLp(w)toHLq(wq/p), where0<α<min{n/2,1},n/(n+1)<p≤n/(n+α), and1/q=1/p-α/n.

scholarly journals Boundedness of Singular Integral Operators with Variable Kernels on Weighted Weak Hardy Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Hua Wang
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Hardy Spaces ◽  
Atomic Decomposition ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Variable Kernel ◽  
Decomposition Theory

Let TΩ be the singular integral operator with variable kernel Ω(x,z). In this paper, by using the atomic decomposition theory of weighted weak Hardy spaces, we will obtain the boundedness properties of TΩ on these spaces, under some Dini type conditions imposed on the variable kernel Ω(x,z).

Fourier operators on weighted Hardy spaces

1987 ◽  
Vol 101 (1) ◽  
pp. 113-121
Author(s):  
Hans P. Heinig
Keyword(s):  
Fourier Transform ◽  
Hardy Spaces ◽  
Atomic Decomposition ◽  
Integral Operators ◽  
Muckenhoupt Weight ◽  
Hardy’S Inequality ◽  
Weighted Hardy Spaces ◽  
Hardy's Inequality ◽  
The Fourier Transform

AbstractIn this note we utilize the atomic decomposition of weighted Hardy spaces to prove weighted versions of Hardy's inequality for the Fourier transform with Muckenhoupt weight. The result extends to certain integral operators with homogeneous kernels of degree −1.

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).

Weighted Norm Inequalities for Fractional Integral Operators With Rough Kernel

1998 ◽  
Vol 50 (1) ◽  
pp. 29-39 ◽  
Author(s):  
Yong Ding ◽  
Shanzhen Lu
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Integral Operators ◽  
Rough Kernel ◽  
Degree Zero ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities ◽  
Fractional Integral Operators ◽  
Image Position

AbstractGiven function Ω on ℝn , we define the fractional maximal operator and the fractional integral operator by and respectively, where 0 < α < n. In this paper we study the weighted norm inequalities of MΩα and TΩα for appropriate α, s and A(p, q) weights in the case that Ω∈ Ls(Sn-1)(s> 1), homogeneous of degree zero.

scholarly journals FRACTIONAL INTEGRAL OPERATORS IN NONHOMOGENEOUS SPACES

2009 ◽  
Vol 80 (2) ◽  
pp. 324-334 ◽  
Author(s):  
H. GUNAWAN ◽  
Y. SAWANO ◽  
I. SIHWANINGRUM
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Type Inequality ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Fractional Integral Operator ◽  
Homogeneous Type ◽  
Fractional Integral Operators

AbstractWe discuss here the boundedness of the fractional integral operatorIαand its generalized version on generalized nonhomogeneous Morrey spaces. To prove the boundedness ofIα, we employ the boundedness of the so-called maximal fractional integral operatorIa,κ*. In addition, we prove an Olsen-type inequality, which is analogous to that in the case of homogeneous type.

scholarly journals Estimates of Fractional Integral Operators on Variable Exponent Lebesgue Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Canqin Tang ◽  
Qing Wu ◽  
Jingshi Xu
Keyword(s):  
Integral Operator ◽  
Maximal Operator ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Weak Type ◽  
Type Inequality ◽  
Integral Operators ◽  
Lebesgue Spaces ◽  
Fractional Integral Operators ◽  
Variable Exponent Lebesgue Spaces

By some estimates for the variable fractional maximal operator, the authors prove that the fractional integral operator is bounded and satisfies the weak-type inequality on variable exponent Lebesgue spaces.

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

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