Cím: | The Ces\`aro operator is bounded on the Hardy space $H\sp 1$. |
Szerző: | Dang Vu Giang; M\'oricz, Ferenc |
Forrás: | Acta Sci. Math. 61, No.1-4, 535-544 (1995). |
Nyelv: | English |
Absztrakt: | The authors define the continuous Ces\`aro operator on integrable
functions on $\bbfR$ by $g= {\cal C}(f)$, where $$\widehat g(t)=
\cases {1\over t} \int^t_0 \widehat f(\xi) d\xi\quad &\text{if}\quad
t\ne 0,\\ 0\quad &\text{if}\quad t= 0\endcases$$ and $\widehat
f$ denotes the Fourier transform. The main result is that $\cal
C$ is bounded on the real Hardy space $H^1(\bbfR)$. The proof
is simple and based on the fact that if $f\in L^1(\bbfR)$ and
$\widehat f(t)= 0$ for $t\le 0$ then $f\in H^1(\bbfR)$, along
with the closed graph theorem.}
\RV{A.G.Siskakis (Thessaloniki) |
Letöltés: | | Zentralblatt |