Uniformly bounded set-valued Nemytskij operators acting between generalized Hölder function spaces

2012 ◽  
Vol 10 (2) ◽  
pp. 609-618 ◽  
Author(s):  
Janusz Matkowski ◽  
Małgorzata Wróbel
Keyword(s):  
Function Spaces ◽  
Bounded Set ◽  
Nemytskij Operators ◽  
Uniformly Bounded

scholarly journals The space of totally bounded analytic functions

1987 ◽  
Vol 30 (2) ◽  
pp. 229-246
Author(s):  
Alan L. Horwitz ◽  
Lee A. Rubel
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Bounded Analytic Functions ◽  
Sharp Bounds ◽  
Totally Bounded ◽  
Bounded Set ◽  
Inverse Interpolation ◽  
Derivatives Of ◽  
Uniformly Bounded

This paper is a continuation of our project on “inverse interpolation”, begun in [6]. In brief, the task of inverse interpolation is to deduce some property of a function f from some given property of the set L of its Lagrange interpolants. In the present work, the property of L is that it be a uniformly bounded set of functions when restricted to the domain of f. In particular (see Section 3), when the domain is a disc, we deduce sharp bounds on the successive derivatives of f. As a result, f must extend to be an analytic function (of restricted growth) in the concentric disc of thrice the original radius.

Bounded weight modules of the Lie algebra of vector fields on ℂ2

2017 ◽  
Vol 16 (12) ◽  
pp. 1750236 ◽  
Author(s):  
Andrew Cavaness ◽  
Dimitar Grantcharov
Keyword(s):  
Lie Algebra ◽  
Vector Fields ◽  
Classification Result ◽  
New Family ◽  
Bounded Set ◽  
Tensor Formula ◽  
Uniformly Bounded ◽  
Weight Modules

We study weight modules of the Lie algebra [Formula: see text] of vector fields on [Formula: see text]. A classification of all simple weight modules of [Formula: see text] with a uniformly bounded set of weight multiplicities is provided. To achieve this classification, we introduce a new family of generalized tensor [Formula: see text]-modules. Our classification result is an important step in the classification of all simple weight [Formula: see text]-modules with finite weight multiplicities.

scholarly journals Uniformly bounded set-valued composition operators in the spaces of functions of bounded variation in the sense of Wiener

2015 ◽  
Vol 14 (4) ◽  
pp. 41-51
Author(s):  
José Atilio Guerrero ◽  
◽  
Janusz Matkowski ◽  
Nelson Merentes ◽  
Małgorzata Wróbel ◽  
...  
Keyword(s):  
Bounded Variation ◽  
Composition Operators ◽  
Functions Of Bounded Variation ◽  
Bounded Set ◽  
Uniformly Bounded
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