Marco Vignati

Equiconvergence theorems for Fourier-Bessel expansions with applications to the harmonic analysis of radial functions in Euclidean and non-Euclidean spaces

We shall prove an equiconvergence theorem between Fourier-Bessel expansions of functions in certain weighted Lebesgue spaces and the classical cosine Fourier expansions of suitable related functions. These weighted Lebesgue spaces arise naturally in the harmonic analysis of radial functions on euclidean spaces and we shall use the equiconvergence result to deduce shag results for the pointwise almost everywhere convergence of Fourier integrals of radial functions in the Lorentz spaces L p,q (R n ). Also we shall briefly apply the above approach to the study of the harmonic analysis of radial functions on noneuclidean hyperbolic spaces

Bochner-Riesz means of functions in weak-Lp

AbstractThe Bochner-Riesz means of order δ≥0 for suitable test functions on ℝN are defined via the Fourier transform by

Some remarks on the weak maximum principle

(S_R^\delta f)(\xi ) = (1 - |\xi |^2 /R^2 )^\delta + \hat f(\xi )

Tangential Boundary Behaviour of Harmonic Functions on Trees

. We show that the means of the critical index

A Local Limit Property for Pattern Statistics in Bicomponent Stochastic Models

\delta = \frac{N}{p} - \frac{{N + 1}}{2},1< p< \frac{{2N}}{{N + 1}}

A Liouville type theorem for a general class of operators on complete manifolds

, do not mapLp,∞(ℝN) intoLp,∞(ℝN), but they map radial functions ofLp,∞(ℝN) intoLp,∞(ℝN). Moreover, iff is radial and in theLp,∞(ℝN) closure of test functions,SRδf(x) converges, asR→+∞, tof(x) in norm and for almost everyx in ℝN. We also observe that the means of the function|x|−N/p, which belongs toLp,∞(ℝN) but not to the closure of test functions, converge for nox.