Salvador Rodríguez-López

Estimates for rough Fourier integral and pseudodifferential operators and applications to the boundedness of multilinear operators

We study the boundedness of rough Fourier integral and pseudodifferential operators, defined by general rough Hormander class amplitudes, on Banach and quasi-Banach LpLp spaces. Thereafter we apply the aforementioned boundedness in order to improve on some of the existing boundedness results for Hormander class bilinear pseudodifferential operators and certain classes of bilinear (as well as multilinear) Fourier integral operators. For these classes of amplitudes, the boundedness of the aforementioned Fourier integral operators turn out to be sharp. Furthermore we also obtain results for rough multilinear operators.

A new class of restricted type spaces

We find new properties for the space R(X), introduced by Soria in the study of the best constant for the Hardy operator minus the identity. In particular, we characterize when R(X) coincides with the minimal Lorentz space Λ(X). The condition that R(X) ≠ {0} is also described in terms of the embedding (L1, ∞ ∩ L∞) ⊂ X. Finally, we also show the existence of a minimal rearrangement-invariant Banach function space (RIBFS) X among those for which R(X) ≠ {0} (which is the RIBFS envelope of the quasi-Banach space L1, ∞ ∩ L∞).

On The Boundedness Of Certain Bilinear Oscillatory Integral Operators

We prove the global L2 × L2 → L1 boundedness of bilinear oscillatory integral operators with amplitudes satisfying a Hormander type condition and phases satisfying appropriate growth as well as the strong non-degeneracy conditions. This is an extension of the corresponding result of R. Coifman and Y. Meyer for bilinear pseudo-differential operators, to the case of oscillatory integral operators.

Restriction results for multilinear multipliers in weighted settings

We obtain restriction results of K. de Leeuws type for maximal operators defined through multilinear Fourier multipliers of either strong or weak type acting on weighted Lebesgue spaces. We give some application of our development. In particular we obtain periodic weighted results for Coifman-Meyer, Hormander and Hormander-Mihlin type multilinear multipliers.

A homomorphism theorem for bilinear multipliers

In this paper, we prove an abstract homomorphism theorem for bilinear multipliers in the setting of locally compact Abelian (LCA) groups. We also provide some applications. In particular, we obtain a bilinear abstract version of de Leeuws theorem for bilinear multipliers of strong and weak types. We also obtain necessary conditions on bilinear multipliers on non-compact LCA groups, yielding boundedness for the corresponding operators on products of rearrangement invariant spaces. Our investigations extend some existing results in ℝn to the framework of general LCA groups, and yield new boundedness results for bilinear multipliers in quasi-Banach spaces.

Multi-parameter extensions of a theorem of Pichorides

Extending work of Pichorides and Zygmund to the

A Seeger–Sogge–Stein theorem for bilinear Fourier integral operators ☆

d

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

-dimensional setting, we show that the supremum of

Transference of local to global

L^p

L^2

-norms of the Littlewood-Paley square function over the unit ball of the analytic Hardy spaces