Search results for "Singular integral"
showing 9 items of 29 documents
The Bochner and Riesz integral representations for the Radon transform
1984
A nicely behaved singular integral on a purely unrectifiable set
2001
We construct an example of a purely 1-unrectifiable AD-regular set E in the plane such that the limit
Maximal potentials, maximal singular integrals, and the spherical maximal function
2014
We introduce a notion of maximal potentials and we prove that they form bounded operators from L to the homogeneous Sobolev space Ẇ 1,p for all n/(n − 1) < p < n. We apply this result to the problem of boundedness of the spherical maximal operator in Sobolev spaces.
A symmetric Galerkin BEM for plate bending analysis
2009
Abstract The Symmetric Galerkin Boundary Element Method is employed in thin plate bending analysis in accordance with the Love–Kirchhoff kinematical assumption. The equations are obtained through the stationary conditions of the total potential energy, written for a plate whose boundary is discretized in boundary elements. Since the matrix coefficients are made up as double integrals with high order singularities, a strategy is shown to compute these coefficients in closed form. Furthermore, in order to model the kinematical discontinuities and to weight the mechanical quantities along the boundary elements, the Lagrangian quadratic shape functions, rather than C 1 type (spline, Hermitian),…
Tangent Measures, Densities, and Singular Integrals
1995
We introduce tangent measures in the sense of David Preiss. We discuss their applications to the density and rectifiability properties of general Borel measures in ℝ n as well as to the behaviour of certain singular integrals with respect to such measures.
Off-diagonal estimates for bi-parameter commutators
2022
Tutkimme kahden parametrin singulaari-integraalien kommutaattoreiden rajoit-tuneisuutta iteroitujen avaruuksien[b, T]:Lp1Lp2→Lq1Lq2välillä kunqi, pi∈(1,∞)ja erityisesti fraktionaalisessa tilanteessaqi6=pi. Yhteensä seitsemässä ta-pauksessa yhdeksästä saavutamme täyden karaterisoinnin rajoittuneisuudella symboliabkoskevillaoskillatorisilla testiehdoilla. We study the boundedness of commutators of bi-parameter singular integrals between mixed spaces [b,T]:Lp1Lp2→Lq1Lq2 in the off-diagonal situation qi,pi∈(1,∞) where we allow qi≠pi. Boundedness is fully characterized in terms of oscillatory testing conditions on the function b for a total seven out of the nine possible arrangements of the inte…
Ω-symmetric measures and related singular integrals
2021
Two examples related to conical energies
2022
In a recent article we introduced and studied conical energies. We used them to prove three results: a characterization of rectifiable measures, a characterization of sets with big pieces of Lipschitz graphs, and a sufficient condition for boundedness of nice singular integral operators. In this note we give two examples related to sharpness of these results. One of them is due to Joyce and M\"{o}rters, the other is new and could be of independent interest as an example of a relatively ugly set containing big pieces of Lipschitz graphs.