DOI10.2307/2118585zbMath0897.42007OpenAlexW2320104342WikidataQ56813983 ScholiaQ56813983MaRDI QIDQ1924340
Joan Verdera, Mark S. Melnikov, Pertti Mattila
Publication date: 7 April 1998
Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2307/2118585
The Huovinen transform and rectifiability of measures ⋮
Nonnegative kernels and 1-rectifiability in the Heisenberg group ⋮
Carleson measure estimates and \(\varepsilon\)-approximation for bounded harmonic functions, without Ahlfors regularity assumptions ⋮
Painlevé's problem and the semiadditivity of analytic capacity. ⋮
The \(Tb\)-theorem on non-homogeneous spaces. ⋮
Singular integrals on \(C_{w^\ast}^{1,\alpha}\) regular curves in Banach duals ⋮
High-dimensional Menger-type curvatures. II: \(d\)-separation and a menagerie of curvatures ⋮
Sublinear measures, Menger curvature, and Hausdorff dimension ⋮
Cones, rectifiability, and singular integral operators ⋮
Singular integrals on \(C^{1, \alpha}\) regular curves in Carnot groups ⋮
Reflectionless measures for Calderón-Zygmund operators. I: General theory ⋮
Singular integrals, analytic capacity and rectifiability ⋮
On some knot energies involving Menger curvature ⋮
Potential theory with multivariate kernels ⋮
The Cauchy integral in \(\mathbb{C}^n\) for domains with minimal smoothness ⋮
Characterization of \(n\)-rectifiability in terms of Jones' square function. II ⋮
Necessary condition for the L2 boundedness of the Riesz transform on Heisenberg groups ⋮
On local properties of singular integrals ⋮
Singular integrals on Ahlfors-David regular subsets of the Heisenberg group ⋮
Calderón-Zygmund capacities and Wolff potentials on Cantor sets ⋮
Principal values for the signed Riesz kernels of non-integer dimension ⋮
Some Calderón-Zygmund kernels and their relations to Wolff capacities and rectifiability ⋮
Capacities associated with Calderón-Zygmund kernels ⋮
Calderón-Zygmund kernels and rectifiability in the plane ⋮
$L^p$ estimates for the variation for singular integrals on uniformly rectifiable sets ⋮
Mass transport and uniform rectifiability ⋮
\(L^2\)-boundedness of gradients of single layer potentials for elliptic operators with coefficients of Dini mean oscillation-type ⋮
Harmonic measure and quantitative connectivity: geometric characterization of the \(L^p\)-solvability of the Dirichlet problem ⋮
An analyst's traveling salesman theorem for sets of dimension larger than one ⋮
Cauchy transforms of self-similar measures: Starlikeness and univalence ⋮
BMO solvability and absolute continuity of harmonic measure ⋮
Cauchy independent measures and almost-additivity of analytic capacity ⋮
Conditions quantitatives de rectifiabilité ⋮
Menger curvature and $C^{1}$ regularity of fractals ⋮
On the \(T(1)\)-theorem for the Cauchy integral ⋮
Reflectionless measures for Calderón-Zygmund operators. II: Wolff potentials and rectifiability ⋮
Unboundedness of potential dependent Riesz transforms for totally irregular measures ⋮
Dahlberg's theorem in higher co-dimension ⋮
Variation for the Riesz transform and uniform rectifiability ⋮
On the uniform rectifiability of AD-regular measures with bounded Riesz transform operator: the case of codimension 1 ⋮
\(L^2\)-boundedness of the Cauchy integral operator for continuous measures ⋮
The Riesz Transform of Codimension Smaller Than One and the Wolff Energy ⋮
A nicely behaved singular integral on a purely unrectifiable set ⋮
Symmetrization of a Cauchy-like kernel on curves ⋮
A new family of singular integral operators whose \(L^2\)-boundedness implies rectifiability ⋮
The measures with an associated square function operator bounded in \(L^2\) ⋮
Menger curvature and rectifiability in metric spaces ⋮
Symmetry theorems and uniform rectifiability ⋮
Large sets of zero analytic capacity ⋮
The weak-\(A_\infty\) property of harmonic and \(p\)-harmonic measures implies uniform rectifiability ⋮
A symmetry theorem revisited ⋮
Singular Integrals on Self-similar Subsets of Metric Groups ⋮
Caloric measure in parabolic flat domains ⋮
Uniform rectifiability and harmonic measure. II: Poisson kernels in \(L^p\) imply uniform rectifiability ⋮
On the existence of principal values for the Cauchy integral on weighted Lebesgue spaces for non-doubling measures ⋮
High-dimensional Menger-type curvatures. I: Geometric multipoles and multiscale inequalities ⋮
Square functions and uniform rectifiability ⋮
Geometry and Hardy spaces on spaces of homogeneous type in the sense of Coifman and Weiss ⋮
A two weight local \(Tb\) theorem for the Hilbert transform ⋮
\(L^2\)-boundedness of gradients of single-layer potentials and uniform rectifiability ⋮
Differentiable points of Sierpinski-like sponges ⋮
Cauchy integral and singular integral operator over closed Jordan curves ⋮
L^2-bounded singular integrals on a purely unrectifiable set in R^d ⋮
On \(d\)-dimensional \(d\)-semimetrics and simplex-type inequalities for high-dimensional sine functions ⋮
On a conjecture of Mergelyan ⋮
Convergence of singular integrals with general measures ⋮
A singular integral approach to a two phase free boundary problem ⋮
Geometric characterizations of embedding theorems: for Sobolev, Besov, and Triebel-Lizorkin spaces on spaces of homogeneous type -- via orthonormal wavelets ⋮
Characterizations of countably \(n\)-rectifiable Radon measures by higher-dimensional Menger curvatures ⋮
A family of singular integral operators which control the Cauchy transform ⋮
Menger curvatures and \(C^{1,\alpha}\) rectifiability of measures ⋮
A new elliptic measure on lower dimensional sets ⋮
Quantitative absolute continuity of harmonic measure and the Dirichlet problem: a survey of recent progress ⋮
Thomson’s theorem on mean square polynomial approximation ⋮
Gradient of the single layer potential and quantitative rectifiability for general Radon measures ⋮
Hausdorff measure and capacity associated with Cauchy potentials ⋮
Finite square function implies integer dimension ⋮
A set with finite curvature and projections of zero length ⋮
LEAST SQUARES APPROXIMATIONS OF MEASURES VIA GEOMETRIC CONDITION NUMBERS ⋮
Recent developments in two weight testing theory ⋮
Singular integrals unsuitable for the curvature method whose \(L^2\)-boundedness still implies rectifiability ⋮
Accretive system \(Tb\)-theorems on nonhomogeneous spaces. ⋮
Reflectionless Measures and the Mattila-Melnikov-Verdera Uniform Rectifiability Theorem ⋮
Removable sets for Lipschitz harmonic functions on Carnot groups ⋮
Boundedness and applications of singular integrals and square functions: a survey ⋮
On the local in time well-posedness of an elliptic-parabolic ferroelectric phase-field model
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