CONVERGENCE OF EVENLY CONTINUOUS NETS IN GENERAL FUNCTION SPACES

1992 ◽  
Vol 18 (2) ◽  
pp. 459 ◽  
Author(s):  
Poppe
Keyword(s):  
Function Spaces ◽  
General Function

General function spaces, products and continuous lattices

1986 ◽  
Vol 100 (2) ◽  
pp. 193-205 ◽  
Author(s):  
John Isbell
Keyword(s):  
General Result ◽  
Metric Spaces ◽  
Function Spaces ◽  
Partial Result ◽  
General Function ◽  
Compact Open Topology ◽  
Locally Compact ◽  
Compact Spaces ◽  
Continuous Lattices ◽  
Locally Compact Spaces

The compact–open topology for function spaces is usually attributed to R. H. Fox in 1945 [16]; and indeed, there is no earlier publication to attribute it to. But it is clear from Fox's paper that the idea of the compact–open topology, and its notable success in locally compact spaces, were already familiar. The topology of course goes back to Riemann; and to generalize to locally compact spaces needs only a definition or two. The actual contributions of Fox were (1) to formulate the partial result, and the problem of extending it, clearly and categorically; (2) to show that in separable metric spaces there is no extension beyond locally compact spaces; (3) to anticipate, partially and somewhat awkwardly, the idea of changing the category so as to save the functorial equation. (Scholarly reservations: Fox attributes the question to Hurewicz, and doubtless Hurewicz had a share in (1). As for (2), when Fox's paper was published R. Arens was completing a dissertation which gave a more general result [1] – though worse formulated.)

A unified method for maximal truncated Calderón–Zygmund operators in general function spaces by sparse domination

2019 ◽  
Vol 63 (1) ◽  
pp. 229-247
Author(s):  
Theresa C. Anderson ◽  
Bingyang Hu
Keyword(s):  
General Setting ◽  
Function Spaces ◽  
Weighted Norm ◽  
General Function ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Weighted Norm Inequalities ◽  
Banach Function Spaces ◽  
Norm Inequalities ◽  
Unified Method

AbstractIn this note we give simple proofs of several results involving maximal truncated Calderón–Zygmund operators in the general setting of rearrangement-invariant quasi-Banach function spaces by sparse domination. Our techniques allow us to track the dependence of the constants in weighted norm inequalities; additionally, our results hold in ℝn as well as in many spaces of homogeneous type.

Embedding of Dirichlet type spaces into tent spaces and Volterra operators

2020 ◽  
pp. 1-12
Author(s):  
Ruishen Qian ◽  
Xiangling Zhu
Keyword(s):  
Integral Operators ◽  
Essential Norm ◽  
Function Spaces ◽  
General Function ◽  
Tent Spaces ◽  
Dirichlet Type ◽  
Volterra Operators ◽  
Type Spaces ◽  
Inclusion Mapping ◽  
Dirichlet Type Spaces

Abstract In this paper, we study the boundedness and compactness of the inclusion mapping from Dirichlet type spaces $\mathcal {D}^{p}_{p-1 }$ to tent spaces. Meanwhile, the boundedness, compactness, and essential norm of Volterra integral operators from Dirichlet type spaces $\mathcal {D}^{p}_{p-1 }$ to general function spaces are also investigated.

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