Continuity for maximal commutator of Bochner-Riesz operators on some weighted Hardy spaces.
Let be a collection of bounded open sets in ℝⁿ such that, for any x ∈ ℝⁿ, there exists a set U ∈ of arbitrarily small diameter containing x. The collection is said to be a density basis provided that, given a measurable set A ⊂ ℝⁿ, for a.e. x ∈ ℝⁿ we have for any sequence of sets in containing x whose diameters tend to 0. The geometric maximal operator associated to is defined on L¹(ℝⁿ) by . The halo function ϕ of is defined on (1,∞) by and on [0,1] by ϕ(u) = u. It is shown that the halo...
In this paper, we obtain some strong and weak type continuity properties for the maximal operator associated with the commutator of the Bochner-Riesz operator on Hardy spaces, Hardy type spaces and weak Hardy type spaces.
We determine the convolution operators on the real analytic functions in one variable which admit a continuous linear right inverse. The characterization is given by means of a slowly decreasing condition of Ehrenpreis type and a restriction of hyperbolic type on the location of zeros of the Fourier transform μ̂(z).
We prove three theorems on linear operators induced by rearrangement of a subsequence of a Haar system. We find a sufficient and necessary condition for to be continuous for 0 < p < ∞.
In this work we define and study wavelets and continuous wavelet transform on semisimple Lie groups G of real rank l. We prove for this transform Plancherel and inversion formulas. Next using the Abel transform A on G and its dual A*, we give relations between the continuous wavelet transform on G and the classical continuous wavelet transform on Rl, and we deduce the formulas which give the inverse operators of the operators A and A*.
On montre que si est une contraction à spectre dénombrable et telle que, pour tout