Fernando Soria

Regularity of solutions of the fractional porous medium flow

We study a porous medium equation with nonlocal diusion eects given by an inverse fractional Laplacian operator. More precisely,

The Mehler Maximal Function: a Geometric Proof of the Weak Type 1

The weak type 1 for the Mehler maximal function is studied via a precise estimate for the ‘maximal kernel’. This, in turn, allows the geometry involved in this setting to be described.

Estimates for the Kakeya Maximal Operator on Radial Functions in Rn

For a real number N > 1, the Kakeya maximal operator K N is defined on locally integrable functions fof R n as

Mean convergence of orthogonal Fourier series of modified functions

{K_N}f\left( x \right) = \mathop {\sup }\limits_{x \in R \in {B_N}} \frac{1}{{\left| R \right|}}\int {_R} \left| {f\left( y \right)} \right|dy

Sharp estimates for the non-centered maximal operator associated to Gaussian and other radial measures

where B N denotes the class of all rectangles in R n of eccentricity N, that is, congruent with any dilate of the rectangle [0,1]n-1x [0, N], and where x007C;Ax007C; represents the Lebesgue measure of the set A.

SOME REMARKS ON RESTRICTION OF THE FOURIER TRANSFORM FOR GENERAL MEASURES

AbstractThe main goal of this work is to prove that every non-negative strong solutionu(x, t) to the problem

Estimates of averages of Fourier transforms with respect to general measures

u_t + (-\Delta)^{\alpha/2}{u} = 0 \,\, {\rm for} (x, t) \in {\mathbb{R}^n} \times (0, T ), \, 0 < \alpha < 2,