# Intrinsic square functions on functions spaces including weighted Morrey spaces

@article{Feuto2012IntrinsicSF, title={Intrinsic square functions on functions spaces including weighted Morrey spaces}, author={Justin Feuto}, journal={arXiv: Classical Analysis and ODEs}, year={2012} }

We prove that the intrinsic square functions including Lusin area integral and Littlewood-Paley $g^{\ast}_{\lambda}$-function as defined by Wilson, are bounded in a class of function spaces include weighted Morrey spaces. The corresponding commutators generated by $BMO$ functions are also considered.

## 12 Citations

Some estimates of intrinsic square functions on the weighted Herz-type Hardy spaces

- Mathematics
- 2010

In this paper, by using the atomic decomposition theory of weighted Herz-type Hardy spaces, we obtain some strong type and weak type estimates for intrinsic square functions including the Lusin area…

On the Multilinear Singular Integrals and Commutators in the Weighted Amalgam Spaces

- Mathematics
- 2014

This paper is concerned with the norm estimates for the multilinear singular integral operators and their commutators formed by BMO functions on the weighted amalgam spaces . Some criterions of…

Pre-Dual of Fofana’s Spaces

- MathematicsMathematics
- 2019

The purpose of this paper is to characterize the pre-dual of the spaces introduced by I. Fofana on the basis of Wiener amalgam spaces. These spaces have a specific dilation behaviour similar to the…

Estimates for Fractional Integral Operators and Linear Commutators on Certain Weighted Amalgam Spaces

- Mathematics
- 2017

In this paper, we first introduce some new classes of weighted amalgam spaces. Then we give the weighted strong-type and weak-type estimates for fractional integral operators $I_\gamma$ on these new…

Two-Weight, Weak-Type Norm Inequalities for a Class of Sublinear Operators on Weighted Morrey and Amalgam Spaces

- Mathematics
- 2017

Let $\mathcal T_\alpha~(0\leq\alpha<n)$ be a class of sublinear operators satisfying certain size conditions introduced by Soria and Weiss, and let $[b,\mathcal T_\alpha]~(0\leq\alpha<n)$ be the…

Estimates for vector-valued intrinsic square functions and their commutators on certain weighted amalgam spaces

- Mathematics
- 2017

In this paper, we first introduce some new kinds of weighted amalgam spaces. Then we deal with the vector-valued intrinsic square functions, which are given by \begin{equation*} \mathcal…

Some estimates for $\theta$-type Calder\'on-Zygmund operators and linear commutators on certain weighted amalgam spaces

- Mathematics
- 2017

In this paper, we first introduce some new kinds of weighted amalgam spaces. Then we discuss the strong type and weak type estimates for a class of Calder\'on--Zygmund type operators $T_\theta$ in…

Some Estimates for θ-type Calderón–Zygmund Operators and Linear Commutators on Certain Weighted Amalgam Spaces

- Mathematics
- 2021

In this paper, we first introduce some new kinds of weighted amalgam spaces. Then we discuss the strong type and weak type estimates for a class of Calderón–Zygmund type operators Tθ in these new…

Two-Weight, Weak-Type Norm Inequalities for Fractional Integral Operators and Commutators on Weighted Morrey and Amalgam Spaces

- Mathematics
- 2018

Let $0<\gamma<n$ and $I_\gamma$ be the fractional integral operator of order $\gamma$, $I_{\gamma}f(x)=\int_{\mathbb R^n}|x-y|^{\gamma-n}f(y)\,dy$, and let $[b,I_\gamma]$ be the linear commutator…

Boundedness of Intrinsic Littlewood-Paley Functions on Musielak-Orlicz Morrey and Campanato Spaces

- Mathematics
- 2013

Let $\varphi: {\mathbb R^n}\times [0,\infty)\to[0,\infty)$ be such that $\vz(x,\cdot)$ is nondecreasing, $\varphi(x,0)=0$, $\varphi(x,t)>0$ when $t>0$, $\lim_{t\to\infty}\varphi(x,t)=\infty$ and…

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