Two-weighted estimates for positive operators and Doob maximal operators on filtered measure spaces

2020 ◽  
Vol 72 (3) ◽  
pp. 795-817 ◽  
Author(s):  
Wei CHEN ◽  
Chunxiang ZHU ◽  
Yahui ZUO ◽  
Yong JIAO
Keyword(s):  
Positive Operators ◽  
Maximal Operators ◽  
Weighted Estimates ◽  
Measure Spaces

scholarly journals Weighted Vector-Valued Inequalities for a Class of Multilinear Singular Integral Operators

2018 ◽  
Vol 61 (2) ◽  
pp. 413-436 ◽  
Author(s):  
Guoen Hu ◽  
Kangwei Li
Keyword(s):  
Singular Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Maximal Operators ◽  
Weighted Estimates ◽  
Multilinear Singular Integral ◽  
Multiple Weights ◽  
Vector Valued

AbstractIn this paper, some weighted vector-valued inequalities with multiple weights $A_{\vec P}$ (ℝmn)are established for a class of multilinear singular integral operators. The weighted estimates for the multi(sub)linear maximal operators which control the multilinear singular integral operators are also considered.

scholarly journals DICHOTOMY PROPERTY FOR MAXIMAL OPERATORS IN A NONDOUBLING SETTING

2018 ◽  
Vol 99 (03) ◽  
pp. 454-466
Author(s):  
DARIUSZ KOSZ
Keyword(s):  
Maximal Operators ◽  
Metric Measure Spaces ◽  
Full Spectrum ◽  
Measure Spaces ◽  
Arbitrary Norm

We investigate a dichotomy property for Hardy–Littlewood maximal operators, noncentred $M$ and centred $M^{c}$ , that was noticed by Bennett et al. [‘Weak- $L^{\infty }$ and BMO’, Ann. of Math. (2) 113 (1981), 601–611]. We illustrate the full spectrum of possible cases related to the occurrence or not of this property for $M$ and $M^{c}$ in the context of nondoubling metric measure spaces $(X,\unicode[STIX]{x1D70C},\unicode[STIX]{x1D707})$ . In addition, if $X=\mathbb{R}^{d}$ , $d\geq 1$ , and $\unicode[STIX]{x1D70C}$ is the metric induced by an arbitrary norm on $\mathbb{R}^{d}$ , then we give the exact characterisation (in terms of $\unicode[STIX]{x1D707}$ ) of situations in which $M^{c}$ possesses the dichotomy property provided that $\unicode[STIX]{x1D707}$ satisfies some very mild assumptions.

scholarly journals Positive operators and maximal operators in a filtered measure space

2013 ◽  
Vol 264 (4) ◽  
pp. 920-946 ◽  
Author(s):  
Hitoshi Tanaka ◽  
Yutaka Terasawa
Keyword(s):  
Measure Space ◽  
Positive Operators ◽  
Maximal Operators

scholarly journals Weighted estimates for fractional maximal functions related to spherical means

2002 ◽  
Vol 66 (1) ◽  
pp. 75-90 ◽  
Author(s):  
Michael Cowling ◽  
José García-Cuerva ◽  
Hendra Gunawan
Keyword(s):  
Mellin Transform ◽  
Maximal Functions ◽  
Maximal Operators ◽  
Spherical Means ◽  
Surface Measure ◽  
Weighted Estimates

We prove weighted Lp-Lq estimates for the maximal operators ℳα, given by , where μt denotes the normalised surface measure on the sphere of centre 0 and radius t in Rd. The techniques used involve interpolation and the Mellin transform. To do this, we also prove weighted Lp-Lq estimates for the operators of convolution with the kernels |·|−α−iη.

scholarly journals Fractional Maximal Functions in Metric Measure Spaces

2013 ◽  
Vol 1 ◽  
pp. 147-162 ◽  
Author(s):  
Toni Heikkinen ◽  
Juha Lehrbäck ◽  
Juho Nuutinen ◽  
Heli Tuominen
Keyword(s):  
Maximal Function ◽  
Lipschitz Function ◽  
Measure Space ◽  
Continuous Functions ◽  
Maximal Operators ◽  
Metric Measure Spaces ◽  
Hölder Continuous ◽  
Fractional Maximal Function ◽  
Measure Spaces ◽  
Hölder Continuous Functions

Abstract We study the mapping properties of fractional maximal operators in Sobolev and Campanato spaces in metric measure spaces. We show that, under certain restrictions on the underlying metric measure space, fractional maximal operators improve the Sobolev regularity of functions and map functions in Campanato spaces to Hölder continuous functions. We also give an example of a space where fractional maximal function of a Lipschitz function fails to be continuous.

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