Cesàro averaging operators on Hardy spaces

1996 ◽  
Vol 126 (3) ◽  
pp. 617-624 ◽  
Author(s):  
Kenneth F. Andersen
Keyword(s):  
Hardy Spaces ◽  
Averaging Operators ◽  
Averaging Operator ◽  
Cesaro Averaging ◽  
Open Question

It is shown that the Cesàro averaging operatorℜα > – 1, satisfies an inequality which immediately implies that it is bounded on certain Hardy spaces including Hp, 0 < p < ∞. This answers an open question of Stempak, who introduced these operators and obtained their boundedness on Hp, 0 < p ≦ 2, for ℜα ≧ 0. The operator which is conjugate to on H2 is also shown to be bounded on Hp for 1 < p < ∞ and ℜα = – 1. This extends a result of Stempak who obtained this boundedness for 2 ≦ p≦ ∞ and ℜα ≧:0.

Adjoint of generalized Cesáro operators on analytic function spaces

2020 ◽  
Vol 26 (2) ◽  
pp. 185-192
Author(s):  
Sunanda Naik ◽  
Pankaj K. Nath
Keyword(s):  
Analytic Function ◽  
Convolution Operator ◽  
Composition Operators ◽  
Mixed Norm ◽  
Averaging Operators ◽  
Mixed Norm Spaces ◽  
Cesaro Averaging ◽  
Analytic Function Spaces ◽  
Appl Math ◽  
Two Parameter

AbstractIn this article, we define a convolution operator and study its boundedness on mixed-norm spaces. In particular, we obtain a well-known result on the boundedness of composition operators given by Avetisyan and Stević in [K. Avetisyan and S. Stević, The generalized Libera transform is bounded on the Besov mixed-norm, BMOA and VMOA spaces on the unit disc, Appl. Math. Comput. 213 2009, 2, 304–311]. Also we consider the adjoint {\mathcal{A}^{b,c}} for {b>0} of two parameter families of Cesáro averaging operators and prove the boundedness on Besov mixed-norm spaces {B_{\alpha+(c-1)}^{p,q}} for {c>1}.

Hardy spaces on ZN

2002 ◽  
Vol 132 (1) ◽  
pp. 25-43 ◽  
Author(s):  
Santiago Boza ◽  
María J. Carro
Keyword(s):  
Maximal Function ◽  
Hardy Spaces ◽  
Atomic Decomposition ◽  
Classical Case ◽  
Positive Answer ◽  
Riesz Transforms ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Definition Of ◽  
Open Question

The work of Coifman and Weiss concerning Hardy spaces on spaces of homogeneous type gives, as a particular case, a definition of Hp(ZN) in terms of an atomic decomposition.Other characterizations of these spaces have been studied by other authors, but it was an open question to see if they can be defined, as it happens in the classical case, in terms of a maximal function or via the discrete Riesz transforms.In this paper, we give a positive answer to this question.

Cesàro averaging operators

1994 ◽  
Vol 124 (1) ◽  
pp. 121-126 ◽  
Author(s):  
Krzysztof Stempak
Keyword(s):  
Sequence Spaces ◽  
Averaging Operators ◽  
Cesaro Averaging

We define a family of Cesàro operators , Reα≧0, and consider the question of their boundedness on Hp spaces. We also consider discrete versions of these operators acting on sequence spaces.

scholarly journals Averaging operators on the ring of continuous functions on a compact space

1964 ◽  
Vol 4 (3) ◽  
pp. 293-298 ◽  
Author(s):  
Barron Brainerd
Keyword(s):  
Compact Space ◽  
Linear Transformation ◽  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Continuous Functions ◽  
Topological Product ◽  
Averaging Operators ◽  
Averaging Operator ◽  
Ring Of Continuous Functions ◽  
Image Position

In this note we answer the following question: Given C(X) the latticeordered ring of real continuous functions on the compact Hausdorff space X and T an averaging operator on C(X), under what circumstances can X be decomposed into a topological product such that supports a measure m and Tf = h where By an averaging operator we mean a linear transformation T on C(X) such that: 1. T is positive, that is, if f>0 (f(x) ≧ 0 for all x ∈ and f(x) > 0 for some a ∈ X), then Tf>0. 2. T(fTg) = (Tf)(Tg). 3. T l = 1 where l(x) = 1 for all x ∈ X.

Research on the Comprehensive Evaluation in Enterprise Operation Environment with Normal Distribution Interval Number

2016 ◽  
Vol 13 (10) ◽  
pp. 7342-7346 ◽  
Author(s):  
Biao Zhang ◽  
Zu-Wei Yu ◽  
Ji-Shu Shao
Keyword(s):  
Normal Distribution ◽  
Choquet Integral ◽  
Comprehensive Evaluation ◽  
Interval Number ◽  
Interval Numbers ◽  
Averaging Operators ◽  
Averaging Operator ◽  
Special Cases ◽  
Multi Attribute Decision Making ◽  
Operation Environment

In this paper, we use the Choquet integral to propose the normal distribution interval number Choquet ordered averaging operator. The operator not only considers the importance of the elements, but also can reflect the correlations among the elements. It is worth pointing out that most of the existing normal distribution interval numbers averaging operators are special cases of our operator. Finally an illustrative example for comprehensive evaluation in enterprise operation environment with normal distribution interval number is given to use the operator in the range of uncertain multi-attribute decision-making. The results show that the method proposed in this paper is feasible.

scholarly journals Averaging operators over nondegenerate quadratic surfaces in finite fields

2015 ◽  
Vol 27 (2) ◽  
Author(s):  
Doowon Koh
Keyword(s):  
Finite Fields ◽  
Averaging Operators ◽  
Averaging Operator ◽  
Quadratic Surfaces

AbstractWe study mapping properties of the averaging operator related to the variety

Averaging Operators and C(X)-Spaces with the Separable Projection Property

1976 ◽  
Vol 28 (5) ◽  
pp. 897-904 ◽  
Author(s):  
John Warren Baker ◽  
John Wolfe
Keyword(s):  
Banach Space ◽  
Lower Bound ◽  
Continuous Function ◽  
Projection Property ◽  
Averaging Operators ◽  
Bounded Linear ◽  
Linear Projection ◽  
Continuous Map ◽  
Averaging Operator ◽  
Projection Constant

The Banach space of bounded continuous real or complexvalued functions on a topological space X is denoted C(X). An averaging operator for an onto continuous function ϕ : X → Y is a bounded linear projection of C(X) onto the subspace ﹛ƒ ∈ C(X) : f is constant on each set ϕ -1(y) for y ∈ Y﹜. The projection constant p(ϕ) for an onto continuous map ϕ is the lower bound for the norms of all averaging operators for ϕ ﹛p(ϕ) = ∞ if there is no averaging operator for ϕ).

scholarly journals Restricted averaging operators to cones over finite fields

2018 ◽  
Vol 30 (6) ◽  
pp. 1345-1361
Author(s):  
Doowon Koh ◽  
Chun-Yen Shen ◽  
Seongjun Yeom
Keyword(s):  
Finite Fields ◽  
Dimensional Subspace ◽  
Surface Measure ◽  
Averaging Operators ◽  
Counting Measure ◽  
Dimensional Vector Space ◽  
Averaging Operator ◽  
Optimal Estimates ◽  
Complex Valued ◽  
Odd Dimensions

AbstractWe investigate the sharp{L^{p}\to L^{r}}estimates for the restricted averaging operator{A_{C}}over the coneCof thed-dimensional vector space{\mathbb{F}_{q}^{d}}over the finite field{\mathbb{F}_{q}}withqelements. The restricted averaging operator{A_{C}}for the coneCis defined by the relation{A_{C}f=f\ast\sigma|_{C}}, where σ denotes the normalized surface measure on the coneC, andfis a complex-valued function on the space{\mathbb{F}_{q}^{d}}with the normalized counting measuredx. In the previous work [D. Koh, C.-Y. Shen and I. Shparlinski, Averaging operators over homogeneous varieties over finite fields, J. Geom. Anal. 26 2016, 2, 1415–1441], the sharp boundedness of{A_{C}}was obtained in odd dimensions{d\geq 3}, but only partial results were given in even dimensions{d\geq 4}. In this paper we prove the optimal estimates in even dimensions{d\geq 6}in the case when the cone{C\subset\mathbb{F}_{q}^{d}}contains a{{d/2}}-dimensional subspace.

Boundedness of the Cesàro averaging operators on Dirichlet spaces

2004 ◽  
Vol 134 (4) ◽  
pp. 609-616
Author(s):  
Kenneth F. Andersen
Keyword(s):  
Dirichlet Space ◽  
Dirichlet Spaces ◽  
Averaging Operators ◽  
Cesaro Averaging ◽  
Associated Operators

It is shown that the Cesàro averaging operators Cα, Re α > −1, introduced by Stempak, are bounded on the Dirichlet space Da if and only if a > 0, while the associated operators Aα are bounded on Da if and only if −1 < a < 2. This extends results of Galanopoulos, who considered the particular case α = 0 for 0 ≤ a ≤ 1.

scholarly journals Boundedness of generalized Cesáro averaging operators on certain function spaces

2005 ◽  
Vol 180 (2) ◽  
pp. 333-344 ◽  
Author(s):  
M.R. Agrawal ◽  
P.G. Howlett ◽  
S.K. Lucas ◽  
S. Naik ◽  
S. Ponnusamy
Keyword(s):  
Function Spaces ◽  
Averaging Operators ◽  
Cesaro Averaging
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