Corrigendum to “On multilinear fractional strong maximal operator associated with rectangles and multiple weights” [Rev. Mat. Iberoam. 33 (2017), no. 2, 555–572]

2018 ◽  
Vol 34 (1) ◽  
pp. 475-479
Author(s):  
Mingming Cao ◽  
Qingying Xue ◽  
Kôzô Yabuta
Keyword(s):  
Maximal Operator ◽  
Multiple Weights ◽  
Strong Maximal Operator

scholarly journals BEST CONSTANTS IN THE WEAK-TYPE ESTIMATES FOR UNCENTERED MAXIMAL OPERATORS

2012 ◽  
Vol 54 (3) ◽  
pp. 655-663
Author(s):  
ADAM OSȨKOWSKI
Keyword(s):  
Maximal Operator ◽  
Borel Measure ◽  
Weak Type ◽  
Integrable Function ◽  
Maximal Operators ◽  
Weak Type Estimates ◽  
Locally Integrable Function ◽  
Image Position ◽  
Strong Maximal Operator ◽  
General Product

AbstractLet μ be a Borel measure on ℝ. The paper contains the proofs of the estimates and Here A is a subset of ℝ, f is a μ-locally integrable function, μ is the uncentred maximal operator with respect to μ and cp,q, and Cp,q are finite constants depending only on the parameters indicated. In the case when μ is the Lebesgue measure, the optimal choices for cp,q and Cp,q are determined. As an application, we present some related tight bounds for the strong maximal operator on ℝn with respect to a general product measure.

Extrapolation to product Herz spaces and some applications

2021 ◽  
Vol 33 (5) ◽  
pp. 1097-1123
Author(s):  
Mingquan Wei
Keyword(s):  
Integral Operator ◽  
Maximal Operator ◽  
Herz Space ◽  
Herz Spaces ◽  
Nirenberg Inequality ◽  
The One ◽  
Strong Maximal Operator ◽  
Strong Fractional Maximal Operator ◽  
Extrapolation Theory

Abstract This paper extends the extrapolation theory to product Herz spaces. To prove the main result, we first investigate the dual space of the product Herz space, and then show the boundedness of the strong maximal operator on product Herz spaces. By using this extrapolation theory, we establish the John–Nirenberg inequality, the characterization of little bmo, the Fefferman–Stein vector-valued inequality, the boundedness of the bi-parameter singular integral operator, the strong fractional maximal operator, and the bi-parameter fractional integral operator on product Herz spaces. We also give a new characterization of little bmo via the boundedness of the commutators of some bi-parameter operators on product Herz spaces. Even in the one-parameter setting, some of our results are new.

scholarly journals A note on the strong maximal operator on Rn

2004 ◽  
Vol 165 (3) ◽  
pp. 291-294 ◽  
Author(s):  
Jiecheng Chen ◽  
Xiangrong Zhu
Keyword(s):  
Maximal Operator ◽  
Strong Maximal Operator

scholarly journals Note on the strong maximal operator

1983 ◽  
Vol 76 (3) ◽  
pp. 225-248
Author(s):  
Marcelo Gómez
Keyword(s):  
Maximal Operator ◽  
Strong Maximal Operator

On Strong Maximal Operators Corresponding to Different Frames

1996 ◽  
Vol 3 (1) ◽  
pp. 81-96
Author(s):  
G. Oniani
Keyword(s):  
General Solution ◽  
Maximal Operator ◽  
Maximal Operators ◽  
Strong Maximal Operator

Abstract The problem is posed and solved whether the conditions and sup θ∈[0,π/2) ∫{M 2, θ (ƒ) > 1} M 2, θ (ƒ) < ∞ are equivalent for functions (where M 2, θ denotes the strong maximal operator corresponding to the frame {OXθ, OYθ }). The results obtained represent a general solution of M. de Guzmán's problem that was previously studied by various authors.

The maximal operator of the Marcinkiewicz-Fejér means of the 2-dimensional Vilenkin-Fourier series

2008 ◽  
Vol 45 (3) ◽  
pp. 321-331
Author(s):  
István Blahota ◽  
Ushangi Goginava
Keyword(s):  
Fourier Series ◽  
Hardy Space ◽  
Maximal Operator ◽  
Fejér Means

In this paper we prove that the maximal operator of the Marcinkiewicz-Fejér means of the 2-dimensional Vilenkin-Fourier series is not bounded from the Hardy space H2/3 ( G2 ) to the space L2/3 ( G2 ).

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