Jim Wright | Searcharxiv

arXiv2025

A priori estimates of Mizohata-Takeuchi type for the Navier-Lam\'e operator

The Mizohata-Takeuchi conjecture for the resolvent of the Navier-Lam\'e equation is a weighted estimate with weights in the so-called Mizohata-Takeuchi class for this operator when one approaches the spectrum (Limiting Absorption Principles). We prove this conjecture in dimensions 2 and 3 for weights with a radial majorant in the Mizohata-Takeuchi class. This result can be seen as an extension of the analogue for the Laplacian given in [8]. We also prove that radial weights in this class are not invariant for the Hardy-Littlewood maximal function, hence the methods in [6] used to extend estimates for the Laplacian to the Navier-Lam\'e case, do not work.

math.AP↗

arXiv2002

$L^p$ improving bounds for averages along curves

We establish local $(L^p,L^q)$ mapping properties for averages on curves. The exponents are sharp except for endpoints.

math.CA↗

arXiv2000

Endpoint multiplier theorems of Marcinkiewicz type

We establish sharp (H^1, L^{1,q}) and local (L \log^r L, L^{1,q}) mapping properties for rough one-dimensional multipliers. In particular, we show that the multipliers in the Marcinkiewicz multiplier theorem map H^1 to L^{1,\infty} and L \log^{1/2} L to L^{1,\infty}, and that these estimates are sharp.

math.CA↗