arXiv subjects

Willian Corrêa

Publications and source records attributed to Willian Corrêa.

4 recordsLinked to original sources

arXiv2026

Interpolation of Directional Banach Spaces and Commutator Estimates

We generalize the complex interpolation formula $(X, X')_{\frac{1}{2}} = L^2$ from the context of Banach function spaces to that of directional Banach spaces. We also obtain a formula for the interpolation of matrix weighted spaces of vector valued functions via interpolation functors, and apply our formula to the particular case of interpolation of matrix weighted $L^p$ spaces by the real and complex methods. We present consequences regarding the matrix Muckenhoupt classes and commutator estimates of Calderón-Zygmund operators with matrix $BMO$ functions. We also characterize the logarithms of Muckenhoupt weights through higher order commutators.

math.FA↗

arXiv2024

Twisted Hilbert spaces defined by bi-Lipschitz maps

We obtain an infinite-dimensional cone of singular twisted Hilbert spaces $Z(φ)$ which are isomorphic to their duals but not to their conjugate duals. We do that by showing that the subset of all bi-Lipschitz maps from $[0, \infty)$ to $\mathbb{R}$ is coneable. We also provide a characterization of the Kalton-Peck space among all twisted Hilbert spaces of the form $Z(φ)$, which gives a partial answer to a conjecture of F. Cabello Sánchez and J. Castillo.

math.FA↗

arXiv2024

Extremes of interpolation scales of Banach spaces

M. Daher gave conditions so that the spheres of the spaces in the interior of a complex interpolation scale are uniformly homeomorphic. We look for sufficient conditions for the validity of this result and related ones on the extremes of the scale, with applications to uniform homeomorphism between spheres of Banach spaces and the sphere of $\ell_2$.

math.FA↗

arXiv2022

Uniform homeomorphisms between spheres induced by interpolation methods

M. Daher [9] showed that if $(X_0, X_1)$ is a regular couple of uniformly convex spaces then the unit spheres of the complex interpolation spaces $X_θ$ and $X_η$ are uniformly homeomorphic for every $0 < θ, η< 1$. We show that this is a rather general phenomenon of interpolation methods described by the discrete framework of interpolation of [15].

math.FA↗