Joint Continuity and Compactness for a Graph Topology in General Function Spaces

1991 ◽  
Vol 152 (1) ◽  
pp. 173-177 ◽  
Author(s):  
Harry Poppe
Keyword(s):  
Function Spaces ◽  
General Function ◽  
Graph Topology ◽  
Joint Continuity

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.)

scholarly journals Graph topology for function spaces

1966 ◽  
Vol 123 (1) ◽  
pp. 267-267 ◽  
Author(s):  
Somashekhar Amrith Naimpally
Keyword(s):  
Function Spaces ◽  
Graph Topology

scholarly journals Joint continuity of function spaces

1970 ◽  
Vol 21 (1) ◽  
pp. 87-89 ◽  
Author(s):  
Paul Ezust
Keyword(s):  
Function Spaces ◽  
Joint Continuity

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.

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