# Javier Pérez LázaroUniversidad de La Rioja (Spain) | UNIRIOJA · Mathematics and Computation

Javier Pérez Lázaro

## About

14

Publications

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268

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Citations since 2017

## Publications

Publications (14)

In this note we describe some recent advances in the area of maximal function
inequalities. We also study the behaviour of the centered Hardy-Littlewood
maximal operator associated to certain families of doubling, radial decreasing
measures, and acting on radial functions. In fact, we precisely determine when
the weak type $(1,1)$ bounds are unifor...

We present a Gagliardo-Nirenberg inequality which bounds Lorentz norms of the
function by Sobolev norms and homogeneous Besov quasinorms with negative
smoothness. We prove also other versions involving Besov or Triebel-Lizorkin
quasinorms. These inequalities can be considered as refinements of Sobolev type
embeddings. They can also be applied to ob...

We obtain pointwise and integral type estimates of higher-order partial moduli of continuity in C via partial derivatives. Also, a Gagliardo–Nirenberg type inequality for partial derivatives in a fixed direction is proved.
Our methods enable us to study the case when different partial derivatives belong to different spaces, including the space
L
1....

We obtain sharp bounds for the modulus of continuity of the uncentered maximal function in terms of the modulus of continuity of the given function, via integral formulas. Some of the results deduced from these formulas are the following: The best constants for Lipschitz and H\"older functions on proper subintervals of $\mathbb{R}$ are $\operatorna...

As shown in [A1], the lowest constants appearing in the weak type (1,1) inequalities satisfied by the centered Hardy-Littlewood maximal operator associated to certain finite radial measures, grow exponentially fast with the dimension. Here we extend this result to a wider class of radial measures and to some values of p>1. Furthermore, we improve t...

We study the Hardy-Littlewood maximal operator defined via an unconditional norm, acting on block decreasing functions. We show that the uncentered maximal operator maps block decreasing functions of special bounded variation to functions with integrable distributional derivatives, thus improving their regularity. In the special case of the maximal...

We show that the lowest constant appearing in the weak type (1,1) inequality
satisfied by the centered Hardy-Littlewood maximal operator on radial
integrable functions is 1.

We prove embedding theorems for fully anisotropic Besov spaces. More concrete, inequalities between modulus of continuity in different metrics and of Sobolev type are obtained. Our goal is to get sharp estimates for some anisotropic cases previously unconsidered.

We study the spaces of functions on Rn for which the generalized partial derivatives exist and belong to different Lorentz spaces Lpk,sk. For this kind of functions we prove a sharp version of the extreme case of the Sobolev embedding theorem using L(∞,s) spaces.

We characterize the space BV(I) of functions of bounded variation on an arbitrary interval I⊂R, in terms of a uniform boundedness condition satisfied by the local uncentered maximal operator MR from BV(I) into the Sobolev space W1,1(I). By restriction, the corresponding characterization holds for W1,1(I). We also show that if U is open in Rd, d>1,...

We prove that if $f:I\subset \Bbb R\to \Bbb R$ is of bounded variation, then the noncentered maximal function $Mf$ is absolutely continuous, and its derivative satisfies the sharp inequality $\|DMf\|_1\le |Df|(I)$. This allows us obtain, under less regularity, versions of classical inequalities involving derivatives. Comment: To appear, TAMS, 21 pa...

La tesis está dedicada a una de las direcciones fundamentales en la teoría general de espacios de funciones - teoremas de inmersión para espacios de funciones diferenciables en varias variables. En primer lugar se estudian inmersiones tipo Sobolev para espacios anisótropos; esto es inmersiones óptimas de espacios de Sobolev en espacios de Lorentz y...