Timeline for Boundedness of integral operators on spaces of continuous functions
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Dec 12, 2019 at 0:00 | history | bounty ended | CommunityBot | ||
| S Dec 12, 2019 at 0:00 | history | notice removed | CommunityBot | ||
| Dec 10, 2019 at 13:06 | history | edited | Delio Mugnolo | CC BY-SA 4.0 |
edited body
|
| Dec 7, 2019 at 17:15 | answer | added | Bazin | timeline score: 2 | |
| Dec 5, 2019 at 13:22 | comment | added | Jochen Wengenroth | In order that $T$ maps the space of bounded continuous functions into itself it is most natural to assume that all $x\mapsto k(x,y)$ are continuous and in addition some assumption allowing to apply the dominated convergence theorem, e.g., for each $x_0\in K$ there are a neighbourhood $A$ and $g\in L^1(\mu)$ such that $|k(x,y)|\le g(y)$ for all $x\in A$ and $y\in K$. | |
| Dec 4, 2019 at 22:47 | comment | added | Delio Mugnolo | @PiotrHajlasz Oh, you're of course right. I've corrected my question accordingly. | |
| Dec 4, 2019 at 22:46 | history | edited | Delio Mugnolo | CC BY-SA 4.0 |
Removed the closure of K from the function spaces I need to consider.
|
| Dec 4, 2019 at 22:36 | comment | added | Piotr Hajlasz | @DelioMugnolo Since $\overline{K}$ is compact,continuous functions are bounded and uniformly bounded (whatever it means). What do you mean by a uuniformly bounded function? | |
| Dec 4, 2019 at 21:44 | comment | added | Delio Mugnolo | @PiotrHajlasz The spaces of bounded continuous functions and bounded uniformly continuous functions, respectively. | |
| Dec 4, 2019 at 13:17 | comment | added | Piotr Hajlasz | What are $C_b$ and $BUC$? | |
| Dec 4, 2019 at 10:33 | history | edited | Delio Mugnolo | CC BY-SA 4.0 |
added 62 characters in body
|
| S Dec 3, 2019 at 22:17 | history | bounty started | Delio Mugnolo | ||
| S Dec 3, 2019 at 22:17 | history | notice added | Delio Mugnolo | Canonical answer required | |
| Nov 28, 2019 at 9:18 | history | edited | Delio Mugnolo | CC BY-SA 4.0 |
explanation of the notation $\overline{K}$
|
| Nov 28, 2019 at 9:17 | comment | added | Delio Mugnolo | @PietroMajer Sorry, by $\overline{K}$ I mean the end compactification. I should have written it; I've edited my question accordingly. Concerning your other question: yes, that's correct. | |
| Nov 28, 2019 at 9:12 | comment | added | Pietro Majer | As I understand you are asking under what conditions $T(X)\subset X$ for each $X$ you mentioned, namely (i) bounded continuous functions on $\overline K$ (is here $\overline K$ the one-point compactification ?); (ii) bounded uniformly continuous functions on $\overline K$ ; 3) $C_0(K)$= continuous functions vanishing at infinity. Correct? | |
| Nov 28, 2019 at 7:31 | history | asked | Delio Mugnolo | CC BY-SA 4.0 |