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| THE FOURIER SERIES EXPANSIONS OF FUNCTIONSDEFINED ON S-SETS |
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Citation： |
Liang Jinrong,Li Wanshe,Su Feng,Ren Fuyao.THE FOURIER SERIES EXPANSIONS OF FUNCTIONSDEFINED ON S-SETS[J].Chinese Annals of Mathematics B,1997,18(2):201~212 |
| Page view： 924
Net amount： 694 |
Authors： |
Liang Jinrong; Li Wanshe;Su Feng; Ren Fuyao; |
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| Abstract： |
Let $ E $ be a compact $s$-sets of $ R^n$. The authors define an
orthonormal system
$ \Phi $ of functions on $E$ and obtain that, for any $f(x)\in L^1(E,
\Cal H^s)$,
the Fourier series of $f$, with respect to $\Phi $, is equal to
$f(x)$ at $\Cal H^s$-a.e. $x\in E.$ Moreover, for any $ f\in L^p(E,\Cal H^s) \ \ (p\ge 1),$ the partial sums of the
Fourier series, with respect to $\Phi$, of $f$ converges to $f$ in $L^p-$norm. |
Keywords： |
Hausdorff measure, Fourier series, $s$-set,
Generalized graph directed construction |
Classification： |
42A20 |
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