On a problem of Littlewood.
On a property of the Fourier transform.
On a sum of Vinogradov
On a Theorem of Ingham.
On a theorem of Kłosowska about generalised convolutions
On a theorem of Saeki concerning convolution squares of singular measures
If , then there exists a probability measure such that the Hausdorff dimension of the support of is and is a Lipschitz function of class .
On a weak type (1,1) inequality for a maximal conjugate function
In their celebrated paper [3], Burkholder, Gundy, and Silverstein used Brownian motion to derive a maximal function characterization of spaces for 0 < p < ∞. In the present paper, we show that the methods in [3] extend to higher dimensions and yield a dimension-free weak type (1,1) estimate for a conjugate function on the N-dimensional torus.
On Abel summability of multiple Jacobi series
On almost summability of conjugate Fourier series.
On an extrapolation theorem of Carleson-Sjölin type with applications to a.e. convergence of Fourier series
On an infinite linear combination of partial sums of Fourier series
On approximation of functions by generalized Abel--Poisson operators.
On approximation of locally compact groups by finite algebraic systems.
On Baica's trigonometric identity.
On belonging of trigonometric series to Orlicz space.
On Bernstein's Inequality and Kahane's Ultraflat Polynomials.
On Besov-Hardy-Sobolev spaces of analytic functions in the unit disc
On bilinear Littlewood-Paley square functions.
On the real line, let the Fourier transform of kn be k'n(ξ) = k'(ξ-n) where k'(ξ) is a smooth compactly supported function. Consider the bilinear operators Sn(f, g)(x) = ∫ f(x+y)g(x-y)kn(y) dy. If 2 ≤ p, q ≤ ∞, with 1/p + 1/q = 1/2, I prove thatΣ∞n=-∞ ||Sn(f,g)||22 ≤ C2||f||p2||g||q2.The constant C depends only upon k.
On Billard's Theorem for Random Fourier Series
We show that Billard's theorem on a.s. uniform convergence of random Fourier series with independent symmetric coefficients is not true when the coefficients are only assumed to be centered independent. We give some necessary or sufficient conditions to ensure the validity of Billard's theorem in the centered case.
On bounds for the derivates of a complex-valued function on a compact interval.