On weighted inequalities for ergodic operators
Rearrangement and continuity properties of functions on spaces of homogeneous type
Weighted weak type inequalities for certain maximal functions
We give an A_p type characterization for the pairs of weights (w,v) for which the maximal operator Mf(y) = sup 1/(b-a) ʃ_a^b |f(x)|dx, where the supremum is taken over all intervals [a,b] such that 0 ≤ a ≤ y ≤ b/ψ(b-a), is of weak type (p,p) with weights (w,v). Here ψ is a nonincreasing function such that ψ(0) = 1 and ψ(∞) = 0.
On continuity properties of functions with conditions on the mean oscillation
In this paper we study distribution and continuity properties of functions satisfying a vanishing mean oscillation property with a lag mapping on a space of homogeneous type.
On one-sided BMO and Lipschitz functions
Pointwise convergence to the initial data for nonlocal dyadic diffusions
We solve the initial value problem for the diffusion induced by dyadic fractional derivative in . First we obtain the spectral analysis of the dyadic fractional derivative operator in terms of the Haar system, which unveils a structure for the underlying “heat kernel”. We show that this kernel admits an integrable and decreasing majorant that involves the dyadic distance. This allows us to provide an estimate of the maximal operator of the diffusion by the Hardy-Littlewood dyadic maximal operator....
Boundedness of convolution operators with smooth kernels on Orlicz spaces
We study boundedness in Orlicz norms of convolution operators with integrable kernels satisfying a generalized Lipschitz condition with respect to normal quasi-distances of ℝⁿ and continuity moduli given by growth functions.
Maximal function estimates for the parabolic mean value kernel.
Gradual doubling property of Hutchinson orbits
The classical self-similar fractals can be obtained as fixed points of the iteration technique introduced by Hutchinson. The well known results of Mosco show that typically the limit fractal equipped with the invariant measure is a (normal) space of homogeneous type. But the doubling property along this iteration is generally not preserved even when the starting point, and of course the limit point, both have the doubling property. We prove that the elements of Hutchinson orbits possess the doubling...
The dyadic fractional diffusion kernel as a central limit
We obtain the fundamental solution kernel of dyadic diffusions in as a central limit of dyadic mollification of iterations of stable Markov kernels. The main tool is provided by the substitution of classical Fourier analysis by Haar wavelet analysis.
On maximal functions over circular sectors with rotation invariant measures
Given a rotation invariant measure in , we define the maximal operator over circular sectors. We prove that it is of strong type for and we give necessary and sufficient conditions on the measure for the weak type inequality. Actually we work in a more general setting containing the above and other situations.
Page 1