A Sobolev norm equivalence on Fock-type spaces with a mixed norm

2019 ◽  
Vol 65 (6) ◽  
pp. 986-1000
Author(s):  
Hong Rae Cho ◽  
Jeong Min Ha ◽  
Han-Wool Lee
Keyword(s):  
Sobolev Norm ◽  
Mixed Norm ◽  
Type 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.

On mixed norm Bergman–Orlicz–Morrey spaces

2018 ◽  
Vol 25 (2) ◽  
pp. 271-282 ◽  
Author(s):  
Alexey N. Karapetyants ◽  
Stefan G. Samko
Keyword(s):  
Unit Disc ◽  
Fourier Coefficients ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Bergman Projection ◽  
Mixed Norm ◽  
Taylor Coefficients ◽  
Type Spaces ◽  
Radial Variable

Abstract Following the ideas of our previous research, in this paper we continue the study of new Bergman-type spaces on the unit disc with mixed norm in terms of Fourier coefficients. Here we deal with the case where the sequence of norms of Fourier coefficients in the Orlicz–Morrey space in radial variable belongs to {l^{q}} . We study the boundedness of the Bergman projection and provide a description of functions in these spaces via the behavior of their Taylor coefficients.

scholarly journals Weighted Fractional Differentiation Composition Operators from Mixed-Norm Spaces to Weighted-Type Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
D. Borgohain ◽  
S. Naik
Keyword(s):  
Composition Operator ◽  
Composition Operators ◽  
Open Unit ◽  
Mixed Norm ◽  
Fractional Differentiation ◽  
Mixed Norm Space ◽  
Type Spaces ◽  
Analytic Maps ◽  
Weighted Type

Let 𝔻 be an open unit disc in the complex plane ℂ and let φ:𝔻→𝔻 as well as u:𝔻→ℂ be analytic maps. For an analytic function f(z)=∑n=0∞anzn on 𝔻 the weighted fractional differentiation composition operator is defined as (Dφ,uβf)(z)=u(z)f[β](φ(z)), where β≥0, f[β](z)=∑n=0∞(Γ(n+1+β)/Γ(n+1))anzn, and f0z=fz. In this paper, we obtain a characterization of boundedness and compactness of weighted fractional differentiation composition operator from mixed-norm space Hp,q,ϕ to weighted-type space Hμ∞.

scholarly journals New criteria for generalized weighted composition operators from mixed norm spaces into Zygmund-type spaces

Filomat ◽  
2012 ◽  
Vol 26 (6) ◽  
pp. 1171-1178
Author(s):  
Yong Ren
Keyword(s):  
Composition Operators ◽  
Mixed Norm ◽  
Weighted Composition Operators ◽  
Mixed Norm Spaces ◽  
Type Spaces ◽  
Weighted Composition ◽  
New Criteria ◽  
Generalized Weighted Composition Operators

New criteria for the boundedness and the compactness of the generalized weighted composition operators from mixed norm spaces into Zygmund-type spaces are given in this paper.

scholarly journals О КЛАССАХ ТИПА ХАРДИ В НЕКОТОРЫХ ОБЛАСТЯХ В Cn И СВЯЗАННЫЕ С НИМИ ПРОБЛЕМЫ

2019 ◽  
pp. 12-37
Author(s):  
R.F. Shamoyan ◽  
V.V. Loseva
Keyword(s):  
Unit Ball ◽  
Hardy Spaces ◽  
Bergman Spaces ◽  
Poisson Integral ◽  
Pseudoconvex Domains ◽  
Mixed Norm ◽  
Convex Domains ◽  
Hardy Type ◽  
Type Spaces ◽  
Decomposition Theorems

We discuss some new problems in several new mixed norm Hardy type spaces in products of bounded pseudoconvex domains with smooth boundary in Cnand then prove some new sharp decomposition theorems for multifunctional Hardy type spaces in the unit ball and then we show also similar results in pseudoconvex and convex domains of finite type extending previously known assertions obtained by first author earlier in Bergman spaces under certain Poisson integral type condition which vanishes in one functional case. Some new (in particular sharp in the unit ball) embeddings for some new mixed norm Hardy spaces in bounded pseudoconvex domains will be also indicated. Some new extensions of Poisson integral in the unit ball and some new assertions concerning them will be indicated and discussed in product domains. Some related multifunctional results are also given.Some new embedding theorems are also provided in some new mixed norm Hardy spaces in unbounded tubular domains over symmetric cones. Введены несколько новых шкал пространств типа Харди со смешанной нормой в единичном шаре, в ограниченных псевдовыпуклых областях и в трубчатых областях над симметрическими конусами в Cn. В этих пространствах обобщающих известное пространство Харди обсуждаются различные задачи. Для пространств такого типа в единичном шаре приводятся в частности точные многофункциональные теоремы вложения типа Карлесона, приводятся также некоторые многофункциональные максимальные теоремы. В трубчатых и в псевдовыпуклых областях получены некоторые прямые аналоги и частичные обобщения этих теорем вложения. При одном дополнительном интегральном условии получены теоремы декомпозиции для весовых мультифункциональных пространств Харди в областях указанного типа,обобщающие ранее известные теоремы такого рода в случае обычных однофункциональных весовых пространств Харди. Ранее первым автором теоремы такого типа были получены в многофункциональных пространствах Бергмана. Наконец вводится прямое обобще ние интеграла типа Пуассона в произведении единичных шаров в Cnи обсуждаются некоторые задачи и обобщения известных результатов связанные с ним.

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