×

On the order of magnitude of the double Fourier transform. (English) Zbl 1479.42028

From the introduction: In this paper, we estimate the order of magnitude of the double Fourier transform for functions of bounded variation (in the sense of Hardy) defined on \(\mathbb R^2\). The result of this paper can be considered to be the nonperiodic version of the results proved by V. Fülöp and F. Móricz [Acta Math. Hung. 104, No. 1–2, 95–104 (2004; Zbl 1067.42006)] for double Fourier coefficients.

MSC:

42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type

Citations:

Zbl 1067.42006
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Fülöp, V.; Móricz, F., Acta Math. Hungar., 104, 1-2, 95-104 (2004) · Zbl 1067.42006 · doi:10.1023/B:AMHU.0000034364.78876.af
[2] Vyas, R. G.; Darji, K. N., Math. Inequal. Appl., 17, 3, 1153-1160 (2014) · Zbl 1292.42006
[3] R. G. Vyas and K. N. Darji, Anal. Theory Appl. 29 (1), 27 (2013). · Zbl 1289.42025
[4] Móricz, F.; Veres, A., Acta Sci. Math. (Szeged), 77, 1-2, 175-190 (2013) · Zbl 1299.42008
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.