This article is cited in 4 scientific papers (total in 4 papers)
On convergence of Riesz spherical means of multiple Fourier series
B. I. Golubov
An $N$-dimensional analog is proved of a theorem of Plessner and Ul'yanov on equivalent conditions for convergence of certain series and integrals. There is obtained from it a sufficient condition on the quadratic modulus of continuity of a periodic function of $N\geqslant2$ variables ensuring the a.e. convergence of the spherical sums of its Fourier series. A two-dimensional analog of a theorem of Luzin and Denjoy and an $N$-dimensional analog of the Dini–Lipschitz criterion are proved. A necessary and sufficient condition on a function $\Phi(u)$ is derived ensuring the pointwise convergence of the Riesz spherical means of critical order of multiple Fourier series of functions of bounded $\Phi$-variation.
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Mathematics of the USSR-Sbornik, 1975, 25:2, 177–197
MSC: Primary 42A20, 42A92; Secondary 42A28, 26A15, 26A45
B. I. Golubov, “On convergence of Riesz spherical means of multiple Fourier series”, Mat. Sb. (N.S.), 96(138):2 (1975), 189–211; Math. USSR-Sb., 25:2 (1975), 177–197
Citation in format AMSBIB
\paper On convergence of Riesz spherical means of multiple Fourier series
\jour Mat. Sb. (N.S.)
\jour Math. USSR-Sb.
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B. I. Golubov, “On the summability of Fourier integrals by Riesz spherical means”, Math. USSR-Sb., 33:4 (1977), 501–518
Christopher Meaney, “On almost-everywhere convergent eigenfunction expansions of the Laplace–Beltrami operator”, Math Proc Camb Phil Soc, 92:1 (1982), 129
M. I. Dyachenko, “Some problems in the theory of multiple trigonometric series”, Russian Math. Surveys, 47:5 (1992), 103–171
M. I. Dyachenko, “$U$-convergence almost everywhere of double Fourier series”, Sb. Math., 186:1 (1995), 47–64
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