We prove sharp power-weighted L, weak type and restricted weak type inequalities for the heat and Poisson integral maximal operators, Riesz transform and a Littlewood-Paley type square function, emerging naturally in the harmonic analysis related to Bessel operators.

This article is devoted to study of the autoconvolution equations and generalized Mittag-Leffler functions. These types of equations are given in terms of the Laplace transform convolution of a function with itself. We state new classes of the autoconvolution equations of the first kind and show that the generalized Mittag-Leffler functions are solutions of these types of equations. In view of ...

It is an open conjecture that generalized Bessel functions associated with root systems have a positive product formula for non-negative multiplicity parameters of the associated Dunkl operators. In this paper, a partial result towards this conjecture is proven, namely a positive radial product formula for the non-symmetric counterpart of the generalized Bessel function, the Dunkl kernel. Radia...

in this paper, we establish some new results in ultra bessel sequences and ultra bessel sequences of subspaces. also, we investigate ultra bessel sequences in direct sums of hilbert spaces.specially, we show that {( fi, gi)}∞ i=1 is a an ultra bessel sequencefor hilbert space h ⊕ k if and only if { fi}∞ i=1 and {gi}∞ i=1 are ultrabessel sequences for hilbert spaces h and k, respectively.

This paper explores various interfaces between the class of generalized gamma convolution (GGC) random variables, Dirichlet process mean functionals and phenomena connected to the local time and occupation time of p-skew Bessel processes and bridges discussed in Barlow, Pitman and Yor (1989), Pitman and Yor (1992, 1997b). First, some general calculus for GGC and Dirichlet process means func-tio...