Laura De Carli

Some sharp restriction theorems for homogeneous manifolds

We prove some restriction theorems for flat homogeneous surfaces of codimension greater than one.

A generalization of Bernoulli's inequality

We prove a generalization of Bernoullis inequality and we apply this generalization to sharpen certain Weierstrass product inequalities

Topics in classical analysis and applications in honor of Daniel Waterman

My Academic Life (D Waterman) Reminiscences (L J Lardy & J L Troutman) On Concentrating Idempotents, A Survey (M Ash) Variants of a Selection Principle for Sequences of Regulated and Non-regulated Functions (V V Chystyakov et al.) Local Lp Inequalities for Gegenbauer Polynomials (L De Carli) General Monotone Sequences and Convergence of Trigonometric Series (M Dyachenko & S Tikhonov) Using Integrals of Squares of Certain Real Valued Special Functions to Prove that the Polya Ξ*(z) Function, the Functions Kiz(a), a > 0, and Some Other Entire Functions Have Only Real Zeros (G Gasper) Functions whose Moments Form a Geometric Progression (M E H Ismail & X Li) Characterization of Scaling Functions in a Frame Multiresolution Analysis In H2G (K Kazarian & A San Antolin) An Abstract Coifman-Rochberg-Weiss Commutator Theorem (J Martin & M Milman) Convergence of Greedy Approximation with Regard to the Trigonometric System (V Temlyakov) Functions of Bounded -Variation (F Prus-Wisniowski).

Growth of

For any convex polyhedron W in ℝ m , p ∈ (1,∞), and N > 1, there are constants γ 1 (W, p, m) and γ 2 (W, p,m) such that Similar results hold for more general regions. These results are various special cases of the inequalities where φ(N) = N p(m-1)/2 when p ∈ (1,2m/m+1), φ(N) = N p(m―1)/2 log N when p = 2m/m+1, and φ(N) = N m(p-1) when p > 2m/m+1 where B is a bounded subset of ℝ m with non-empty interior.

L^{p}

We provide L p →L q estimates for a class of Fourier multipliers supported in convex cones of { R } n+1. In particular, we consider cones whose boundary has n−1 nonvanishing principal curvatures and cones which are the convex envelope of N linearly independent half lines passing through the origin of { R } n+1. In some case our estimates are best possible.

Lebesgue constants for convex polyhedra and other regions

We discuss existence and stability of Riesz bases of exponential type of L^2(T) for special domains T called trapezoids. We construct exponential bases on L^2(T) when T is a finite union of rectangles with the same height. We also generalize our main theorems in dimension d\ge 3.

On Fourier Multipliers Over Tube Domains

Let m be a bounded and monotonic function on R with λ=infm and Λ=supm. We study the best constant in the inequality ‖Tmf‖p≤c‖f‖p for 1<p<∞, where Tm is the Fourier multiplier associated to m. Our result is completely explicit when Λ=−λ and when Λ·λ=0. We also discuss the case of m with bounded variation.

Exponential bases on two dimensional trapezoids

We show that the discrete Hilbert transform and the discrete Kak-Hilbert transform are infinitesimal generator of one-parameter groups of operators

On the (p,p) norm of monotonic Fourier multipliers

In this paper we prove the sharp inequality |Pn(s)(x)| = Pn(s)(1) (|x|n + {n-1}/{2 s+1} (1 - |x|n)), where Pn(s)(x) is the classical ultraspherical polynomial of degree n and order s = n frac{1 + v 5}{4}. This inequality can be refined in [0, zns] and [zns, 1], where zns denotes the largest zero of Pn(s) (x).

One-parameter groups of operators and discrete Hilbert transforms

In this paper we prove a unique continuation theorem for elliptic operators of the formP(D)+V(x), whereP(D) has orderm≥2 and simple complex characteristics, andV(x)∈Ln/m(Rn). To prove our main theorem we use a restriction theorem for the Fourier transform to manifolds of codimension 2.