Sufficient conditions for the Lebesgue integrability of double Fourier transforms
We consider complex-valued functions / £ Lp(R2) for some 1 < p < 2 and give sufficient conditions for its Fourier transform / to belong to Lr{{(u,v) £ R2 : |u| > 1 and |u| > 1}), where 0 < r < q and l/p+ l/q = 1. Under additional conditions, we also give sufficient conditions, unde...
Elmentve itt :
| Szerzők: | |
|---|---|
| További közreműködők: | |
| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2013
|
| Sorozat: | Acta scientiarum mathematicarum
79 No. 1-2 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/30869 |
| Tartalmi kivonat: | We consider complex-valued functions / £ Lp(R2) for some 1 < p < 2 and give sufficient conditions for its Fourier transform / to belong to Lr{{(u,v) £ R2 : |u| > 1 and |u| > 1}), where 0 < r < q and l/p+ l/q = 1. Under additional conditions, we also give sufficient conditions, under which we have / £ Lr (R2). These sufficient conditions are in terms of the Lp-integral modulus or the ordinary modulus of continuity of / . Our theorems apply for functions in the Lipschitz classes Lip(ai, a2 ), where 0 < aq, a2 < 1 as well as for functions of bounded s-variation on R2, where 0 < s < p. The results of this paper can be considered to be the nonperiodic versions of those results proved in [5] for double Fourier series, and the latter ones were in turn the two-dimensional extensions of the classical theorems of Bernstein, Szász and Zygmund on the absolute convergence of single Fourier series. |
|---|---|
| Terjedelem/Fizikai jellemzők: | 175-190 |
| ISSN: | 0001-6969 |