scholarly journals Vector-Valued Inequalities in the Morrey Type Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Hua Wang
Keyword(s):  
Maximal Function ◽  
Weak Type ◽  
Growth Function ◽  
Morrey Spaces ◽  
Doubling Condition ◽  
Littlewood Maximal Function ◽  
Weighted Morrey Spaces ◽  
Weak Type Estimates ◽  
Type Spaces ◽  
Vector Valued

We will obtain the strong type and weak type estimates for vector-valued analogues of classical Hardy-Littlewood maximal function, weighted maximal function, and singular integral operators in the weighted Morrey spacesLp,κ(w)when1≤p<∞and0<κ<1, and in the generalized Morrey spacesLp,Φfor1≤p<∞, whereΦis a growth function on(0,∞)satisfying the doubling condition.

scholarly journals Boundedness of Vector-Valued Intrinsic Square Functions in Morrey Type Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Hua Wang
Keyword(s):  
Weak Type ◽  
Growth Function ◽  
Morrey Spaces ◽  
Square Functions ◽  
Doubling Condition ◽  
Weighted Morrey Spaces ◽  
Weak Type Estimates ◽  
Type Spaces ◽  
Vector Valued ◽  
Intrinsic Square Functions

We will obtain the strong type and weak type estimates for vector-valued analogues of intrinsic square functions in the weighted Morrey spacesLp,κ(w)when1≤p<∞,0<κ<1, and in the generalized Morrey spacesLp,Φfor1≤p<∞, whereΦis a growth function on(0,∞)satisfying the doubling condition.

scholarly journals The Boundedness of the Hardy-Littlewood Maximal Operator and Multilinear Maximal Operator in Weighted Morrey Type Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Takeshi Iida
Keyword(s):  
Maximal Function ◽  
Maximal Operator ◽  
Morrey Spaces ◽  
Weighted Morrey Spaces ◽  
Type Spaces ◽  
Multilinear Maximal Function ◽  
Multilinear Maximal Operator ◽  
Littlewood Maximal Operator

The aim of this paper is to prove the boundedness of the Hardy-Littlewood maximal operator on weighted Morrey spaces and multilinear maximal operator on multiple weighted Morrey spaces. In particular, the result includes the Komori-Shirai theorem and the Iida-Sato-Sawano-Tanaka theorem for the Hardy-Littlewood maximal operator and multilinear maximal function.

scholarly journals Fefferman–Stein Inequalities for the Hardy–Littlewood Maximal Function on the Infinite Rooted k-ary Tree

2020 ◽  
Author(s):  
Sheldy Ombrosi ◽  
Israel P Rivera-Ríos ◽  
Martín D Safe
Keyword(s):  
Maximal Function ◽  
Weak Type ◽  
Type Estimate ◽  
Abstract Theorem ◽  
Littlewood Maximal Function ◽  
Infinite Trees ◽  
Vector Valued

Abstract In this paper, weighted endpoint estimates for the Hardy–Littlewood maximal function on the infinite rooted $k$-ary tree are provided. Motivated by Naor and Tao [ 23], the following Fefferman–Stein estimate $$\begin{align*}& w\left(\left\{ x\in T\,:\,Mf(x)&gt;\lambda\right\} \right)\leq c_{s}\frac{1}{\lambda}\int_{T}|f(x)|M(w^{s})(x)^{\frac{1}{s}}\: \text{d}x\qquad s&gt;1\end{align*}$$is settled, and moreover, it is shown that it is sharp, in the sense that it does not hold in general if $s=1$. Some examples of nontrivial weights such that the weighted weak type $(1,1)$ estimate holds are provided. A strong Fefferman–Stein-type estimate and as a consequence some vector-valued extensions are obtained. In the appendix, a weighted counterpart of the abstract theorem of Soria and Tradacete [ 38] on infinite trees is established.

scholarly journals Boundedness ofθ-Type Calderón–Zygmund Operators and Commutators in the Generalized Weighted Morrey Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-18 ◽  
Author(s):  
Hua Wang
Keyword(s):  
Morrey Space ◽  
Weak Type ◽  
Strong Type ◽  
Type Estimate ◽  
Generalized Morrey Space ◽  
Weighted Morrey Space ◽  
Weighted Morrey Spaces ◽  
Weak Type Estimates ◽  
Special Cases ◽  
Type Spaces

We first introduce some new Morrey type spaces containing generalized Morrey space and weighted Morrey space as special cases. Then, we discuss the strong-type and weak-type estimates for a class of Calderón–Zygmund type operatorsTθin these new Morrey type spaces. Furthermore, the strong-type estimate and endpoint estimate of commutators[b,Tθ]formed bybandTθare established. Also, we study related problems about two-weight, weak-type inequalities forTθand[b,Tθ]in the Morrey type spaces and give partial results.

scholarly journals Weak-type Estimates in Morrey Spaces for Maximal Commutator and Commutator of Maximal Function

2018 ◽  
Vol 41 (1) ◽  
pp. 193-218 ◽  
Author(s):  
Amiran GOGATISHVILI ◽  
Rza MUSTAFAYEV ◽  
Müjdat AǦCAYAZI
Keyword(s):  
Maximal Function ◽  
Weak Type ◽  
Morrey Spaces ◽  
Weak Type Estimates

scholarly journals Estimates of Intrinsic Square Functions on Generalized Weighted Morrey Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Guilian Gao ◽  
Xiaomei Wu
Keyword(s):  
Weak Type ◽  
Morrey Spaces ◽  
Strong Type ◽  
Square Functions ◽  
Weighted Morrey Spaces ◽  
Weak Type Estimates ◽  
Intrinsic Square Functions

We prove the boundedness of the intrinsic functions on generalized weighted Morrey spacesMp,φ(w), including the strong type estimates and weak type estimates. Moreover, we define thekth-order commutators generated byBMORnfunctions and intrinsic functions, and obtain their strong type estimates onMp,φ(w). In some cases, we improve previous results.

scholarly journals Weak Type Estimates of Variable Kernel Fractional Integral and Their Commutators on Variable Exponent Morrey Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Xukui Shao ◽  
Shuangping Tao
Keyword(s):  
Lebesgue Space ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Weak Type ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Variable Kernel ◽  
Fractional Integral Operators ◽  
Weak Type Estimates ◽  
Weak Morrey Spaces

In this paper, the authors obtain the boundedness of the fractional integral operators with variable kernels on the variable exponent weak Morrey spaces based on the results of Lebesgue space with variable exponent as the infimum of exponent function p(·) equals 1. The corresponding commutators generated by BMO and Lipschitz functions are considered, respectively.

A note on the one-dimensional maximal function

1989 ◽  
Vol 111 (3-4) ◽  
pp. 325-328 ◽  
Author(s):  
Antonio Bernal
Keyword(s):  
Maximal Function ◽  
Weak Type ◽  
Type Inequality ◽  
Best Constant ◽  
Weak Type Inequality ◽  
One Dimensional ◽  
Littlewood Maximal Function ◽  
The One

SynopsisIn this note, we consider the Hardy-Littlewood maximal function on R for arbitrary measures, as was done by Peter Sjögren in a previous paper. We determine the best constant for the weak type inequality.

The Weak Type (1, 1) Estimates of Maximal Functions on the Laguerre Hypergroup

2010 ◽  
Vol 53 (3) ◽  
pp. 491-502 ◽  
Author(s):  
Jizheng Huang ◽  
Liu Heping
Keyword(s):  
Maximal Function ◽  
Weak Type ◽  
Maximal Functions ◽  
Laguerre Hypergroup ◽  
Littlewood Maximal Function

AbstractIn this paper, we discuss various maximal functions on the Laguerre hypergroup K including the heat maximal function, the Poisson maximal function, and the Hardy–Littlewood maximal function which is consistent with the structure of hypergroup of K. We shall establish the weak type (1, 1) estimates for these maximal functions. The Lp estimates for p > 1 follow fromthe interpolation. Some applications are included.

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