scholarly journals On the radial maximal function of distributions

1986 ◽  
Vol 121 (2) ◽  
pp. 467-483 ◽  
Author(s):  
Akihito Uchiyama
Keyword(s):  
Maximal Function ◽  
Radial Maximal Function

scholarly journals Some Properties of Quasinearly Subharmonic Functions and Maximal Theorem for Bergman Type Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-3
Author(s):  
Olivera R. Mihić
Keyword(s):  
Unit Ball ◽  
Maximal Function ◽  
Subharmonic Functions ◽  
Maximal Theorem ◽  
Type Spaces ◽  
Radial Maximal Function

Let denote the class of quasinearly subharmonic functions in unit ball . We provide, following result: if and if , then , where is the radial maximal function and , and . Also, we prove a maximal theorem for Bergman type spaces.

scholarly journals Maximal characterisation of local Hardy spaces on locally doubling manifolds

2021 ◽  
Author(s):  
Alessio Martini ◽  
Stefano Meda ◽  
Maria Vallarino
Keyword(s):  
Riemannian Manifold ◽  
Maximal Function ◽  
Hardy Spaces ◽  
Integrable Function ◽  
Local Heat ◽  
Metric Measure Spaces ◽  
Measure Spaces ◽  
Local Hardy Spaces ◽  
Atomic Hardy Space ◽  
Radial Maximal Function

AbstractWe prove a radial maximal function characterisation of the local atomic Hardy space $${{\mathfrak {h}}}^1(M)$$ h 1 ( M ) on a Riemannian manifold M with positive injectivity radius and Ricci curvature bounded from below. As a consequence, we show that an integrable function belongs to $${{\mathfrak {h}}}^1(M)$$ h 1 ( M ) if and only if either its local heat maximal function or its local Poisson maximal function is integrable. A key ingredient is a decomposition of Hölder cut-offs in terms of an appropriate class of approximations of the identity, which we obtain on arbitrary Ahlfors-regular metric measure spaces and generalises a previous result of A. Uchiyama.

On the Smirnov Class Defined by the Maximal Function

2002 ◽  
Vol 45 (2) ◽  
pp. 265-271 ◽  
Author(s):  
Marek Nawrocki
Keyword(s):  
Maximal Function ◽  
Linear Functional ◽  
Continuous Linear ◽  
Continuous Linear Functional ◽  
Smirnov Class ◽  
Convex Structure ◽  
Dual Spaces ◽  
Radial Maximal Function ◽  
Locally Convex

AbstractH. O. Kim has shown that contrary to the case of Hp-space, the Smirnov class M defined by the radial maximal function is essentially smaller than the classical Smirnov class of the disk. In the paper we show that these two classes have the same corresponding locally convex structure, i.e. they have the same dual spaces and the same Fréchet envelopes. We describe a general form of a continuous linear functional on M and multiplier from M into Hp, 0 < p ≤ ∞.

scholarly journals REAL-VARIABLE CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BESSEL OPERATORS

2011 ◽  
Vol 09 (03) ◽  
pp. 345-368 ◽  
Author(s):  
DACHUN YANG ◽  
DONGYONG YANG
Keyword(s):  
Maximal Function ◽  
Hardy Spaces ◽  
Riesz Transform ◽  
Real Variable ◽  
Bessel Operator ◽  
Bessel Operators ◽  
Lusin Area Function ◽  
Radial Maximal Function ◽  
Nontangential Maximal Function

Let λ > 0, p ∈ ((2λ + 1)/(2λ + 2), 1], and [Formula: see text] be the Bessel operator. In this paper, the authors establish the characterizations of atomic Hardy spaces Hp((0,∞),dmλ) associated with △λ in terms of the radial maximal function, the nontangential maximal function, the grand maximal function, the Littlewood–Paley g-function and the Lusin-area function, where dmλ(x) ≡ x2λ dx. As an application, the authors further obtain the Riesz transform characterization of these Hardy spaces.

scholarly journals Radial maximal function characterizations for Hardy spaces on RD-spaces

2009 ◽  
Vol 137 (2) ◽  
pp. 225-251 ◽  
Author(s):  
Loukas Grafakos ◽  
Liguang Liu ◽  
Dachun Yang
Keyword(s):  
Maximal Function ◽  
Hardy Spaces ◽  
Radial Maximal Function

scholarly journals Some estimates for the commutators of multilinear maximal function on Morrey-type space

2021 ◽  
Vol 19 (1) ◽  
pp. 515-530
Author(s):  
Xiao Yu ◽  
Pu Zhang ◽  
Hongliang Li
Keyword(s):  
Maximal Function ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Bounded Mean Oscillation ◽  
Generalized Morrey Spaces ◽  
Type Space ◽  
Bmo Function ◽  
Mean Oscillation ◽  
Multilinear Maximal Function ◽  
Equivalent Conditions

Abstract In this paper, we study the equivalent conditions for the boundedness of the commutators generated by the multilinear maximal function and the bounded mean oscillation (BMO) function on Morrey space. Moreover, the endpoint estimate for such operators on generalized Morrey spaces is also given.

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