A trilinear restriction problem for the paraboloid in .
A two weight weak inequality for potential type operators
We give conditions on pairs of weights which are necessary and sufficient for the operator to be a weak type mapping of one weighted Lorentz space in another one. The kernel is an anisotropic radial decreasing function.
A two-weight estimate for a class of fractional integral operators with rough kernel.
A two-weight inequality for the Bessel potential operator
Necessary conditions and sufficient conditions are derived in order that Bessel potential operator is bounded from the weighted Lebesgue spaces into when .
A unified approach to various orthogonalities
A Uniform Estimate for Fourier Transforms of Measures on Polynomial Curves in ...
A uniform estimate for quartile operators.
There is a one parameter family of bilinear Hilbert transforms. Recently, some progress has been made to prove Lp estimates for these operators uniformly in the parameter. In the current article we present some of these techniques in a simplified model...
A unifying approach for certain class of maximal functions.
A universal constant for exponential Riesz sequences.
A Universal Topology for Sequence Spaces.
A variant of compressed sensing.
A variant of Hörmander's conditionfor singular integrals
A variant sharp estimate for multilinear singular integral operators
We establish a variant sharp estimate for multilinear singular integral operators. As applications, we obtain the weighted norm inequalities on general weights and certain type estimates for these multilinear operators.
A variation norm Carleson theorem
We strengthen the Carleson-Hunt theorem by proving estimates for the -variation of the partial sum operators for Fourier series and integrals, for . Four appendices are concerned with transference, a variation norm Menshov-Paley-Zygmund theorem, and applications to nonlinear Fourier transforms and ergodic theory.
A version of the law of large numbers
By the method of Rio [10], for a locally square integrable periodic function f, we prove for almost every x and t > 0.
A wavelet characterization for weighted Hardy spaces.
In this article we give a wavelet area integral characterization for weighted Hardy spaces Hp(ω), 0 < p < ∞, with ω ∈ A∞. Our wavelet characterization establishes the identification between Hp(ω) and T2p (ω), the weighted discrete tent space, for 0 < p < ∞ and ω ∈ A∞. This allows us to use all the results of tent spaces for weighted Hardy spaces. In particular, we obtain the isomorphism between Hp(ω) and the dual space of Hp'(ω), where 1< p < ∞ and 1/p +...
A way of estimating the convergence rate of the Fourier method for PDE of hyperbolic type
The Fourier expansion in eigenfunctions of a positive operator is studied with the help of abstract functions of this operator. The rate of convergence is estimated in terms of its eigenvalues, especially for uniform and absolute convergence. Some particular results are obtained for elliptic operators and hyperbolic equations.
A weak molecule condition for certain Triebel-Lizorkin spaces
A weak molecule condition is given for the Triebel-Lizorkin spaces Ḟ_p^{α,q}, with 0 < α < 1 and 1 < p, q < ∞. As an easy corollary, one may deduce, by atomic-molecular methods, a Triebel-Lizorkin space "T1" Theorem of Han and Sawyer, and Han, Jawerth, Taibleson and Weiss, for Calderón-Zygmund kernels K(x,y) which are not assumed to satisfy any regularity condition in the y variable.
A weak type inequality for Cauchy transforms of finite measures.
In this note we present a simple proof of a recent result of Mattila and Melnikov on the existence of limε→0 ∫|ζ-z|>ε (ζ - z)-1dμ(ζ) for finite Borel measures μ in the plane.
A weighted interpolation problem for analytic functions