estimates for weakly strongly singular integral operators on spaces of homogeneous type
H¹ and BMO for certain locally doubling metric measure spaces of finite measure
In a previous paper the authors developed an H¹-BMO theory for unbounded metric measure spaces (M,ρ,μ) of infinite measure that are locally doubling and satisfy two geometric properties, called “approximate midpoint” property and “isoperimetric” property. In this paper we develop a similar theory for spaces of finite measure. We prove that all the results that hold in the infinite measure case have their counterparts in the finite measure case. Finally, we show that the theory applies to a class...
Hardy spaces and oscillatory singular integrals.
Hardy spaces of conjugate temperatures
We define Hardy spaces of pairs of conjugate temperatures on using the equations introduced by Kochneff and Sagher. As in the holomorphic case, the Hilbert transform relates both components. We demonstrate that the boundary distributions of our Hardy spaces of conjugate temperatures coincide with the boundary distributions of Hardy spaces of holomorphic functions.
Hilbert transform, Toeplitz operators and Hankel operators and invariant A∞ weights.
In this paper, several sufficient conditions for boundedness of the Hilbert transform between two weighted Lp-spaces are obtained. Invariant A∞ weights are obtained. Several characterizations of invariant A∞ weights are given. We also obtain some sufficient conditions for products of two Toeplitz operators of Hankel operators to be bounded on the Hardy space of the unit circle using Orlicz spaces and Lorentz spaces.
Hilbert transforms and maximal functions along rough flat curves.
Homeomorphisms acting on Besov and Triebel-Lizorkin spaces of local regularity ψ(t).
The aim of this paper is to show that the integral and derivative operators defined by local regularities are homeomorphisms for generalized Besov and Triebel-Lizorkin spaces with local regularities. The underlying geometry is that of homogeneous type spaces and the functions defining local regularities belong to a larger class of growth functions than the potentials tα, related to classical fractional integral and derivative operators and Besov and Triebel-Lizorkin spaces.
Homeomorphisms preserving Ap.
Homogeneous estimates for oscillatory integrals.
Homogeneous even kernels on surfaces.
Hubert integrals, Singular integrals, and Radon transforms II.
Hyperbolic singular integral operators.
We define a class of integral operators which are singular relative to the hyperbolic metric in simply connected domains of the plane. We study the necessary and sufficient conditions for such operators to be bounded on L2 of the upper half plane relative to the hyperbolic metric.
Hypersingular Marcinkiewicz integrals along surface with variable kernels on Sobolev space and Hardy-Sobolev space.