On High Precision Methods for the Evaluation of Fourier Integrals with Finite and Infinite Limits.
On Higher Riesz Transforms for Gaussian Measures.
On holomorphy in Banach spaces and absolute convergence of Fourier series
On infinitely smooth almost-wavelets with compact support.
There are known wavelets with exponential decay on infinity [2,3,4] and wavelets with compact support [5]. But these functions have finite smoothness. It is known that there do not exist infinitely differentiable compactly supported wavelets.
On instances of Fox’s integral equation connection to the Riemann zeta function
We consider some applications of the singular integral equation of the second kind of Fox. Some new solutions to Fox’s integral equation are discussed in relation to number theory.
On integrability of functions defined by trigonometric series.
On Integrability of Trigonometric Series with Quasi - Monotone Coefficients
On integral operators with operator-valued kernels.
On summability of Fourier series.
On Jackson type inequality in Orlicz classes.
It is shown that Jackson type inequality fails in the Orlicz classes φ(L) if φ(x) differs essentially from a power function of any order.
On Kahane's ultraflat polynomials
On Kakeya–Nikodym averages, -norms and lower bounds for nodal sets of eigenfunctions in higher dimensions
We extend a result of the second author [27, Theorem 1.1] to dimensions which relates the size of -norms of eigenfunctions for to the amount of -mass in shrinking tubes about unit-length geodesics. The proof uses bilinear oscillatory integral estimates of Lee [22] and a variable coefficient variant of an " removal lemma" of Tao and Vargas [35]. We also use Hörmander’s [20] oscillatory integral theorem and the Cartan–Hadamard theorem to show that, under the assumption of nonpositive curvature,...
On convergence of certain cosine sums.
On -convergence of certain cosine sums with third semi-convex coefficients.
On convergence of certain cosine sums with twice quasi semi-convex coefficients.
On -convergence of certain generalized modified trigonometric sums
On -convergence of Walsh-Fourier series.
On integrability and convergence of trigonometric series
We first give a necessary and sufficient condition for , 1 < p < ∞, 1/p - 1 < γ < 1/p, where ϕ(x) is the sum of either or , under the condition that λₙ (where λₙ is aₙ or bₙ respectively) belongs to the class of so called Mean Value Bounded Variation Sequences (MVBVS). Then we discuss the relations among the Fourier coefficients λₙ and the sum function ϕ(x) under the condition that λₙ ∈ MVBVS, and deduce a sharp estimate for the weighted modulus of continuity of ϕ(x) in norm.
On boundedness for convolutions with kernels having singularities on a sphere
For the convolution operators with symbols , 0 ≤ Re α < n, , we construct integral representations and give the exact description of the set of pairs (1/p,1/q) for which the operators are bounded from to .
On Lacunary Incomplete Polynomials.