Singular Cauchy integrals and conformal welding on Jordan curves.
Singular distributions, dimension of support, and symmetry of Fourier transform
We study the “Fourier symmetry” of measures and distributions on the circle, in relation with the size of their supports. The main results of this paper are:(i) A one-side extension of Frostman’s theorem, which connects the rate of decay of Fourier transform of a distribution with the Hausdorff dimension of its support;(ii) A construction of compacts of “critical” size, which support distributions (even pseudo-functions) with anti-analytic part belonging to .We also give examples of non-symmetry...
Singular integral characterization of nonisotropic generalized BMO spaces
We extend a result of Coifman and Dahlberg [Singular integral characterizations of nonisotropic spaces and the F. and M. Riesz theorem, Proc. Sympos. Pure Math., Vol. 35, pp. 231–234; Amer. Math. Soc., Providence, 1979] on the characterization of spaces by singular integrals of with a nonisotropic metric. Then we apply it to produce singular integral versions of generalized BMO spaces. More precisely, if is the family of dilations in induced by a matrix with a nonnegative eigenvalue, then...
Singular integral operators on manifolds with a boundary.
Singular integral operators on Nakano spaces with weights having finite sets of discontinuities
In 1968, Gohberg and Krupnik found a Fredholm criterion for singular integral operators of the form aP + bQ, where a,b are piecewise continuous functions and P,Q are complementary projections associated to the Cauchy singular integral operator, acting on Lebesgue spaces over Lyapunov curves. We extend this result to the case of Nakano spaces (also known as variable Lebesgue spaces) with certain weights having finite sets of discontinuities on arbitrary Carleson curves.
Singular integral operators with Cauchy kernel in fractional spaces.
Singular integral operators with complex homogeneity
Singular integral operators with non-smooth kernels on irregular domains.
Let χ be a space of homogeneous type. The aims of this paper are as follows.i) Assuming that T is a bounded linear operator on L2(χ), we give a sufficient condition on the kernel of T such that T is of weak type (1,1), hence bounded on Lp(χ) for 1 < p ≤ 2; our condition is weaker then the usual Hörmander integral condition.ii) Assuming that T is a bounded linear operator on L2(Ω) where Ω is a measurable subset of χ, we give a sufficient condition on the kernel of T so that T is of weak type...
Singular Integrals, Analytic Capacity and Rectifiability.
Singular integrals and cardinal series
Singular integrals and rectifiability.
We shall discuss singular integrals on lower dimensional subsets of Rn. A survey of this topic was given in [M4]. The first part of this paper gives a quick review of some results discussed in [M4] and a survey of some newer results and open problems. In the second part we prove some results on the Riesz kernels in Rn. As far as I know, they have not been explicitly stated and proved, but they are very closely related to some earlier results and methods.[Proceedings of the 6th International Conference...
Singular integrals and spherical convergence
Singular integrals and the Newton diagram.
We examine several scalar oscillatory singular integrals involving a real-analytic phase function φ(s,t) of two real variables and illustrate how one can use the Newton diagram of φ to efficiently analyse these objects. We use these results to bound certain singular integral operators.
Singular Integrals in the Cesàro Sense.
Singular integrals in the space Λ(B,X)
Singular integrals in weighted Lebesgue spaces with variable exponent.
Singular integrals on
Singular integrals on generalized Lipschitz and Hardy spaces
Singular integrals on homogeneous spaces and some problems of classical analysis
Singular integrals on Iwasawa NA groups of rank 1.