arXiv subjects

Salvador Rodriguez-Lopez

Publications and source records attributed to Salvador Rodriguez-Lopez.

8 recordsLinked to original sources

arXiv2023

Multipliers for Hardy-Orlicz spaces and applications

Using real-variable methods, we characterise multipliers for general classes of Hardy--Orlicz spaces, unifying and extending several classical results due to Hardy and Littlewood; Duren and Shields; Paley; and others. Applications of our results include inequalities involving Fourier coefficients and Fourier transforms of elements of Hardy--Orlicz spaces and their duals, as well as embeddings into spaces of generalised smoothness, Sobolev type-embeddings and Paley-Wiener type theorems.

math.CA↗

arXiv2023

Multilinear oscillatory integrals and estimates for coupled systems of dispersive PDEs

We establish sharp global regularity of a class of multilinear oscillatory integral operators that are associated to nonlinear dispersive equations with both Banach and quasi-Banach target spaces. As a consequence we also prove the (local in time) continuous dependence on the initial data for solutions of a large class of coupled systems of dispersive partial differential equations.

math.AP↗

arXiv2022

Bilinear pseudodifferential operators with symbol in $BS_{1,1}^m$ on Triebel-Lizorkin spaces with critical Sobolev index

In this paper we obtain new estimates for bilinear pseudodifferential operators with symbol in the class $BS_{1,1}^m$, when both arguments belong to Triebel-Lizorkin spaces of the type $F_{p,q}^{n/p}(\mathbb{R}^n)$. The inequalities are obtained as a consequence of a refinement of the classical Sobolev embedding $F^{n/p}_{p,q}(\mathbb{R}^n)\hookrightarrow\mathrm{bmo}(\mathbb{R}^n)$, where we replace $\mathrm{bmo}(\mathbb{R}^n)$ by an appropriate subspace which contains $L^\infty(\mathbb{R}^n)$. As an application, we study the product of functions on $F_{p,q}^{n/p}(\mathbb{R}^n)$ when $1<p<\infty$, where those spaces fail to be multiplicative algebras.

math.AP↗

arXiv2020

Local and global estimates for hyperbolic equations in Besov-Lipschitz and Triebel-Lizorkin spaces

In this paper we establish optimal local and global Besov-Lipschitz and Triebel-Lizorkin estimates for the solutions to linear hyperbolic partial differential equations. These estimates are based on local and global estimates for Fourier integral operators that span all possible scales (and in particular both Banach and quasi-Banach scales) of Besov-Lipschitz spaces $B^s_{p,q}(\R^n)$, and certain Banach and quasi-Banach scales of Triebel-Lizorkin spaces $F^s_{p,q}(\R^n)$

math.AP↗

arXiv2019

Global boundedness of multilinear Fourier integral operators

We establish global regularity of multilinear Fourier integral operators that are associated to nonlinear wave equations on product of $L^p$ spaces by proving endpoint boundedness on suitable products spaces containing combinations of the local Hardy space, the local BMO and the $L^2$ spaces.

math.AP↗

arXiv2018

Multi-parameter extensions of a theorem of Pichorides

Extending work of Pichorides and Zygmund to the $d$-dimensional setting, we show that the supremum of $L^p$-norms of the Littlewood-Paley square function over the unit ball of the analytic Hardy spaces $H^p_A(\mathbb{T}^d)$ blows up like $(p-1)^{-d}$ as $p\to 1^+$. Furthermore, we obtain an $L\log^d L$-estimate for square functions on $H^1_A(\mathbb{T}^d)$. Euclidean variants of Pichorides's theorem are also obtained.

math.CA↗

arXiv2011

Global boundedness of multilinear Fourier integral operators

We study the global boundedness of bilinear and multilinear Fourier integral operators on Banach and quasi-Banach $L^p$ spaces, where the amplitudes of the operators are smooth or rough in the spatial variables. The results are obtained by proving suitable global boundedness of rough linear Fourier integral operators with amplitudes that behave as $L^{p}$ functions in the spatial variables. The bilinear and multilinear boundedness estimates are proven by using either an iteration procedure or decomposition of the amplitudes, and thereafter applying our global results for linear Fourier integral operators with rough amplitudes.

math.AP↗

arXiv2011

On the boundedness of certain bilinear Fourier integral operators

We prove the global $L^2 \times L^2 \to L^1$ boundedness of bilinear Fourier integral operators with amplitudes in $S^0_{1,0} (n,2)$. To achieve this, we require that the phase function can be written as $(x,ξ,η) \mapsto \phase_1(x,ξ) + \phase_2(x,η)$ where each $\phase_j$ belongs to the class $Φ^2$ and satisfies the strong non-degeneracy condition. This result extends that of R. Coifman and Y. Meyer regarding pseudodifferential operators to the case of Fourier integral operators.

math.AP↗