On generalized localization of Fourier
                    inversion for distributions

Ashurov, Ravshan; Butaev, Almaz

doi:10.1090/conm/672/13549

Cited by 4 publications

(3 citation statements)

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“…For the spherical partial integrals of multiple Fourier integrals the generalized localization principle in Lp(R N ) has been investigated by many authors from 1983 till 2016 (Sjölin, P., Carbery, A., Soria F., Rubio de Francia, J. L., Vega, L., Bastys A., and others (see [11] - [18]).…”

Section: Generalized Localization Principle For the Multiple Fourier ...mentioning

confidence: 99%

“…The authors of the paper [18] obtained the necessary and sufficient conditions for the generalized localization of the Riesz means of distributions to be hold. These conditions are formulated in the following two theorems.…”

Section: Generalized Localization Principle For the Multiple Fourier ...mentioning

confidence: 99%

“…Observe, as mentioned above for E 0 λ f (x) ≡ E λ f (x) the generalized localization holds true for L2-functions. The following theorem (proved in [18]) states, that for a negative order Riesz means the generalized localization fails. Theorem 3.8.…”

Section: Generalized Localization Principle For the Multiple Fourier ...mentioning

confidence: 99%

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Generalized localization for spherical partial sums of multiple Fourier series

Ashurov

2019

Доклады Академии наук

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It is well known, that Luzin's conjecture has a positive solution for one dimensional trigonometric Fourier series and it is still open for the spherical partial sums S λ f (x), f ∈ L 2 (T N ), of multiple Fourier series, while it has the solution for square and rectangular partial sums. Historically progress with solving Luzin's conjecture has been made by considering easier problems. One of such easier problems for S λ f (x) was suggested by V. A. Il'in in 1968 and this problem is called the generalized localization principle. In this paper we first give a short survey on convergence almost-everywhere of Fourier series and on generalized localization of Fourier integrals, then present a positive solution for the generalized localization problem for S λ f (x).

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Section: Generalized Localization Principle For the Multiple Fourier ...mentioning

confidence: 99%

Section: Generalized Localization Principle For the Multiple Fourier ...mentioning

confidence: 99%