Let X be a compact, connected, Riemannian manifold (without boundary), ρ be the geodesic distance on X, μ be a probability measure on X, and {φk} be an orthonormal (with respect to μ) system of continuous functions, φ0(x) = 1 for all x ∈ X, {`k} ∞ k=0 be an nondecreasing sequence of real numbers with `0 = 1, `k ↑ ∞ as k → ∞, ΠL := span {φj : `j ≤ L}, L ≥ 0. We describe conditions to ensure an e...

In this paper, we shall discuss the weighted boundedness of the fractional type Marcinkiewicz integral operators associated to surfaces, and extend a result given by Chen, Fan and Ying in 2002 and the one given by authors. They showed that under certain conditions the fractional type Marcinkiewicz integral operators are bounded from the Triebel-Lizorkin spaces Ḟ pq (R) to L(R). Recently one of ...

The Marcinkiewicz Strong Law, lim n→∞ 1 n 1 p n ∑ k=1 (Dk −D) = 0 a.s. with p ∈ (1, 2), is studied for outer products Dk = XkX T k , where {Xk}, {Xk} are both twosided (multivariate) linear processes (with coefficient matrices (Cl), (Cl) and i.i.d. zero-mean innovations {Ξ}, {Ξ}). Matrix sequences Cl and Cl can decay slowly enough (as |l| → ∞) that {Xk, Xk} have long-range dependence while {Dk}...

In this paper we prove a Marcinkiewicz-type multiplier result for the spherical Fourier transform on products of rank one noncompact symmetric spaces.

Recently, norm equivalences between spherical polynomials and their sample values at scattered sites have been proved. These so-called MarcinkiewiczZygmund inequalities involve a parameter that characterizes the density of the sampling set and they are applicable to all polynomials whose degree does not exceed an upper bound that is determined by the density parameter. We show that if one is sa...

We study extinction profiles of solutions to fast diffusion equations with some initial data in the Marcinkiewicz space. The will be singular their stationary equations.