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

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}.

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.

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.

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.

Averaging Operators and Martingale Inequalities in Rearrangement Invariant Function Spaces

1999 ◽  
Vol 42 (3) ◽  
pp. 321-334
Author(s):  
Masato Kikuchi
Keyword(s):  
Probability Measure ◽  
Invariant Function ◽  
Function Spaces ◽  
Averaging Operators ◽  
Martingale Inequalities ◽  
Rearrangement Invariant Function Spaces ◽  
Change Of Probability Measure

AbstractWe shall study some connection between averaging operators and martingale inequalities in rearrangement invariant function spaces. In Section 2 the equivalence between Shimogaki’s theorem and some martingale inequalities will be established, and in Section 3 the equivalence between Boyd’s theorem andmartingale inequalities with change of probability measure will be established.

scholarly journals The Bohr Inequality for the Generalized Cesáro Averaging Operators

2021 ◽  
Vol 19 (1) ◽  
Author(s):  
Ilgiz R. Kayumov ◽  
Diana M. Khammatova ◽  
Saminathan Ponnusamy
Keyword(s):  
Averaging Operators ◽  
Cesaro Averaging

scholarly journals Geometric Properties of Cesàro Averaging Operators

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Priyanka Sangal ◽  
A. Swaminathan
Keyword(s):  
Analytic Function ◽  
Unit Disc ◽  
Averaging Operators ◽  
Geometric Properties ◽  
Cesaro Averaging

Using positivity of trigonometric cosine and sine sums whose coefficients are generalization of Vietoris numbers, we find the conditions on coefficient {ak} to characterize the geometric properties of the corresponding analytic function f(z)=z+∑k=2∞akzk in the unit disc D. As an application, we also find geometric properties of generalized Cesàro-type polynomials.

Function Spaces and Nonsymmetric Norm Preserving Maps

2018 ◽  
Vol 25 (5) ◽  
pp. 729-740
Author(s):  
Hadis Pazandeh ◽  
Fereshteh Sady
Keyword(s):  
Function Spaces
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