Restricted summability of Fourier series and Hardy spaces
A general summability method, the so-called 0-summability is considered for multi-dimensional Fourier series and Fourier transforms. Under some conditions on 6 we will show that the restricted maximal operator of the 0-means of a distribution is bounded from Hp(Td ) to Lp(T d ) for all po < P_<...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2009
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| Sorozat: | Acta scientiarum mathematicarum
75 No. 1-2 |
| Kulcsszavak: | Matematika, Fourier-sor, Hardy-tér |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16296 |
| Tartalmi kivonat: | A general summability method, the so-called 0-summability is considered for multi-dimensional Fourier series and Fourier transforms. Under some conditions on 6 we will show that the restricted maximal operator of the 0-means of a distribution is bounded from Hp(Td ) to Lp(T d ) for all po < P_< oo and it is of weak type (1,1), provided that the supremum in the maximal operator is taken over a cone-like set. The parameter po < 1 is depending on the dimension, the function 6 and on the cone-like set. As a consequence we obtain a generalization of a well-known result due to Marcinkiewicz and Zygmund, namely, that the d-dimensional 0-means of a function / 6 ¿i(Td converge a.e. to / over the cone-like set. The same results are given for Fourier transforms, too. Some special cases of the 0-summation aire considered, such as the Cesáro, Fejér, Riesz, Riemann, Weierstrass, Picar, Bessel, Rogosinski and de La Vallée-Poussin summations. |
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| Terjedelem/Fizikai jellemzők: | 197-217 |
| ISSN: | 0001-6969 |