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- W4300783061 abstract "For a Lebesgue integrable complex-valued function f defined over the m-dimensional torus $$mathbb{T}^m:=[0,2pi)^m$$ , let $$hat{f}(rm{n})$$ denote the Fourier coefficient of f, where n = (n(1),..., n(m)) ∈ ℤm. Recently, in [Acta Math. Hungar., 128 (2010), 328–343], we have defined the notion of bounded p-variation (p ≥ 1) for a complex-valued function on a rectangle [a1, b1] ×... × [am, bm] and studied the order of magnitude of Fourier coefficients of such functions on [0, 2π]m. In this paper, the order of magnitude of Fourier coefficients of a function of bounded p-variation (p ≥ 1) from [0, 2π]m to ℂ and having lacunary Fourier series with certain gaps is studied and a result analogous to Theorem 2 in [Acta Math. Hungar., 104 (2004), 95–104] and Theorem 2 in [Acta Math. Hungar., 128 (2010), 328–343] is proved." @default.
- W4300783061 created "2022-10-04" @default.
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- W4300783061 date "2012-06-01" @default.
- W4300783061 modified "2023-10-07" @default.
- W4300783061 title "Order of magnitude of multiple Fourier coefficients of functions of bounded p-variation having lacunary Fourier series" @default.
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- W4300783061 doi "https://doi.org/10.1007/bf03651305" @default.
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