Bochner-Riesz means of functions in weak-L p
| ISSN: | 1436-5081 0026-9255 |
|---|---|
| DOI: | 10.1007/bf01311209 |
| Přístupová URL adresa: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a55fd8b5f16752fd6ea5fee767e7e77d https://doi.org/10.1007/bf01311209 |
| Rights: | CLOSED |
| Přírůstkové číslo: | edsair.doi.dedup.....a55fd8b5f16752fd6ea5fee767e7e77d |
| Autor: | Leonardo Colzani, Marco Vignati, Giancarlo Travaglini |
| Přispěvatelé: | Colzani, L, Travaglini, G, Vignati, M |
| Rok vydání: | 1993 |
| Předmět: |
General Mathematics
Mathematical analysis Fourier-Hankel expansion weak-$L\sp p$ test function Bochner-Riesz mean radial function Combinatorics symbols.namesake Fourier transform Lorentz spaces Norm (mathematics) symbols Critical index Fourier-Bessel expansion MAT/05 - ANALISI MATEMATICA Mathematics |
| Zdroj: | Monatshefte f�r Mathematik. 115:35-45 |
| ISSN: | 1436-5081 0026-9255 |
| DOI: | 10.1007/bf01311209 |
| Popis: | The Bochner-Riesz means of order delta greater-than-or-equal-to 0 for suitable test functions on R(N) are defined via the Fourier transform by (S(R)(delta)f)(xi) = (1 - \xi\2/R2)+(delta)f(xi). We show that the means of the critical index delta = N/P - N + 1/2, 1 < p < 2N/N + 1, do not map L(p,infinity)(R(N)) into L(p,infinity) (R(N)), but they map radial functions of L(p,infinity) (R(N)) into L(p,infinity) (R(N)). Moreover, if f is radial and in the L(p,infinity) (R(N)) closure of test functions, S(R)(delta)f (x) converges, as R --> + infinity, to f(x) in norm and for almost every x in R(N). We also observe that the means of the function absolute value of x-N/p, which belongs to L(p,infinity) (R(N)) but not to the closure of test functions, converge for no x |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink