A theory of Besov and Triebel-Lizorkin spaces on metric measure spaces modeled on Carnot-Carathéodory spaces.
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 Uniform Estimate for Fourier Transforms of Measures on Polynomial Curves in ...
A unifying approach for certain class of maximal functions.
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 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 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
A weighted norm inequality for singular integrals
A weighted vector-valued weak type (1,1) inequality and spherical summation
We prove a weighted vector-valued weak type (1,1) inequality for the Bochner-Riesz means of the critical order. In fact, we prove a slightly more general result.
A weighted version of Journé's lemma.
In this paper we discuss a weighted version of Journé's covering lemma, a substitution for Whitney decomposition of an open set in R2 where squares are replaced by rectangles. We then apply this result to obtain a sharp version of the atomic decomposition of the weighted Hardy spaces Hu'p (R+2 x R+2) and a description of their duals when p is close to 1.
A₁-regularity and boundedness of Calderón-Zygmund operators
The Coifman-Fefferman inequality implies quite easily that a Calderón-Zygmund operator T acts boundedly in a Banach lattice X on ℝⁿ if the Hardy-Littlewood maximal operator M is bounded in both X and X'. We establish a converse result under the assumption that X has the Fatou property and X is p-convex and q-concave with some 1 < p, q < ∞: if a linear operator T is bounded in X and T is nondegenerate in a certain sense (for example, if T is a Riesz transform) then M is bounded in both X and...
About a non-homogeneous Hardy-inequality and its relation with the spectrum of Dirac operators
A non-homogeneous Hardy-like inequality has recently been found to be closely related to the knowledge of the lowest eigenvalue of a large class of Dirac operators in the gap of their continuous spectrum.