scholarly journals Note on a Li-Stević integral-type operator from mixed-norm spaces to nth weighted spaces

2017 ◽  
pp. 77-85
Author(s):  
Haiying Li ◽  
Zhi ao Guo
Keyword(s):  
Type Operator ◽  
Weighted Spaces ◽  
Mixed Norm ◽  
Integral Type ◽  
Mixed Norm Spaces

scholarly journals On an Integral-Type Operator from Zygmund-Type Spaces to Mixed-Norm Spaces on the Unit Ball

2010 ◽  
Vol 2010 ◽  
pp. 1-7 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Unit Ball ◽  
Type Operator ◽  
Mixed Norm ◽  
Integral Type ◽  
Mixed Norm Space ◽  
Mixed Norm Spaces ◽  
Norm Space ◽  
Type Spaces

The boundedness and compactness of an integral-type operator recently introduced by the author from Zygmund-type spaces to the mixed-norm space on the unit ball are characterized here.

scholarly journals Approximation by generalized integral Favard-Szász type operators involving Sheffer polynomials

Filomat ◽  
2019 ◽  
Vol 33 (7) ◽  
pp. 1921-1935
Author(s):  
Seda Karateke ◽  
Çiğdem Atakut ◽  
İbrahim Büyükyazıcı
Keyword(s):  
Modulus Of Continuity ◽  
Order Of Convergence ◽  
Type Theorem ◽  
Type Operator ◽  
Weighted Spaces ◽  
Approximation Properties ◽  
Integral Type ◽  
Korovkin Type Theorem ◽  
Numerical Examples ◽  
Sheffer Polynomials

This article deals with the approximation properties of a generalization of an integral type operator in the sense of Favard-Sz?sz type operators including Sheffer polynomials with graphics plotted using Maple. We investigate the order of convergence, in terms of the first and the second order modulus of continuity, Peetre?s K-functional and give theorems on convergence in weighted spaces of functions by means of weighted Korovkin type theorem. At the end of the work, we give some numerical examples.

scholarly journals Embeddings of harmonic mixed norm spaces on smoothly bounded domains in ℝn

2019 ◽  
Vol 17 (1) ◽  
pp. 1260-1268
Author(s):  
Miloš Arsenović ◽  
Tanja Jovanović
Keyword(s):  
Unit Ball ◽  
Bounded Domain ◽  
Maximal Function ◽  
Unit Disc ◽  
Harmonic Functions ◽  
Type Operator ◽  
Mixed Norm ◽  
Bounded Domains ◽  
Function Type ◽  
Mixed Norm Spaces

Abstract The main result of this paper is the embedding $$\begin{array}{} \displaystyle \mathcal{B}^{s,r}_\beta({\it\Omega})\hookrightarrow \mathcal{B}^{s_1,r_1}_{\beta+(n-1)\big(\frac 1s-\frac 1{s_1}\big)}({\it\Omega}), \end{array}$$ 0 < r ≤ r1 ≤ ∞, 0 < s ≤ s1 ≤ ∞, β > –1, of harmonic functions mixed norm spaces on a smoothly bounded domain Ω ⊂ ℝn. We also extend a result on boundedness, in mixed norm, of a maximal function-type operator from the case of the unit disc and the unit ball to general domains in ℝn.

scholarly journals HARDY–BLOCH TYPE SPACES AND LACUNARY SERIES ON THE POLYDISK

2007 ◽  
Vol 49 (2) ◽  
pp. 345-356 ◽  
Author(s):  
K. L. AVETISYAN
Keyword(s):  
Lacunary Series ◽  
Weighted Spaces ◽  
Mixed Norm ◽  
Fractional Operators ◽  
Mixed Norm Spaces ◽  
Sharp Estimates ◽  
Type Spaces ◽  
Unit Polydisk ◽  
The Mean

AbstractWe extend the well-known Paley and Paley-Kahane-Khintchine inequalities on lacunary series to the unit polydisk of $\C^n$. Then we apply them to obtain sharp estimates for the mean growth in weighted spaces h(p, α), h(p, log(α)) of Hardy–Bloch type, consisting of functions n-harmonic in the polydisk. These spaces are closely related to the Bloch and mixed norm spaces and naturally arise as images under some fractional operators.

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