On bounded sets of holomorphic mappings

1974 ◽  
pp. 123-134 ◽  
Author(s):  
Jorge Alberto Barroso ◽  
Mário C. Matos ◽  
Leopoldo Nachbin
Keyword(s):  
Holomorphic Mappings ◽  
Bounded Sets

scholarly journals Locally bounded sets of holomorphic mappings

1988 ◽  
Vol 309 (2) ◽  
pp. 609-609 ◽  
Author(s):  
Jos{é Bonet ◽  
Pablo Galindo ◽  
Domingo Garc{í}a ◽  
Manuel Maestre
Keyword(s):  
Holomorphic Mappings ◽  
Bounded Sets

scholarly journals The Composition Operation on Spaces of Holomorphic Mappings

2020 ◽  
Vol 71 (2) ◽  
pp. 557-572
Author(s):  
María D Acosta ◽  
Pablo Galindo ◽  
Luiza A Moraes
Keyword(s):  
Banach Space ◽  
Complex Banach Space ◽  
Holomorphic Mappings ◽  
Fréchet Space ◽  
Frechet Space ◽  
Linear Subspaces ◽  
Left And Right ◽  
Relationship Of ◽  
The Relationship ◽  
Bounded Sets

Abstract We discuss the continuity of the composition on several spaces of holomorphic mappings on open subsets of a complex Banach space. On the Fréchet space of entire mappings that are bounded on bounded sets, the composition turns out to be even holomorphic. In such a space, we consider linear subspaces closed under left and right composition. We discuss the relationship of such subspaces with ideals of operators and give several examples of them. We also provide natural examples of spaces of holomorphic mappings where the composition is not continuous.

Norm inequalities on variable exponent vanishing Morrey type spaces for the rough singular type integral operators

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ferit Gürbüz ◽  
Shenghu Ding ◽  
Huili Han ◽  
Pinhong Long
Keyword(s):  
Integral Operator ◽  
Singular Integral ◽  
Variable Exponent ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Rough Kernel ◽  
Type Integral ◽  
Type Spaces ◽  
Bounded Sets ◽  
Littlewood Maximal Operator

AbstractIn this paper, applying the properties of variable exponent analysis and rough kernel, we study the mapping properties of rough singular integral operators. Then, we show the boundedness of rough Calderón–Zygmund type singular integral operator, rough Hardy–Littlewood maximal operator, as well as the corresponding commutators in variable exponent vanishing generalized Morrey spaces on bounded sets. In fact, the results above are generalizations of some known results on an operator basis.

Trace inequalities for fractional integrals in mixed norm grand lebesgue spaces

2020 ◽  
Vol 23 (5) ◽  
pp. 1452-1471
Author(s):  
Vakhtang Kokilashvili ◽  
Alexander Meskhi
Keyword(s):  
Riesz Potential ◽  
Fractional Integrals ◽  
Mixed Norm ◽  
Lebesgue Spaces ◽  
Fractional Integral Operators ◽  
Grand Lebesgue Spaces ◽  
Measure Spaces ◽  
Necessary And Sufficient ◽  
Bounded Sets ◽  
Trace Inequalities

Abstract D. Adams type trace inequalities for multiple fractional integral operators in grand Lebesgue spaces with mixed norms are established. Operators under consideration contain multiple fractional integrals defined on the product of quasi-metric measure spaces, and one-sided multiple potentials. In the case when we deal with operators defined on bounded sets, the established conditions are simultaneously necessary and sufficient for appropriate trace inequalities. The derived results are new even for multiple Riesz potential operators defined on the product of Euclidean spaces.

Partition Bounded Sets Into Sets Having Smaller Diameters

2021 ◽  
Vol 76 (3) ◽  
Author(s):  
Yanlu Lian ◽  
Senlin Wu
Keyword(s):  
Bounded Sets

Banach spaces of $l\sp{p}$ valued holomorphic mappings

1973 ◽  
Vol 40 (4) ◽  
pp. 755-763
Author(s):  
James M. Westall, Jr.
Keyword(s):  
Banach Spaces ◽  
Holomorphic Mappings
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