English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We investigate the global continuity on $L^p$ spaces with $p\in [1,\infty]$of Fourier integral operators with smooth and rough amplitudes and/or phasefunctions subject to certain non-degeneracy conditions. We initiate theinvestigation of the continuity of smooth and rough Fourier integral operatorson weighted $L^{p}$ spaces, $L_{w}^p$ with $1< p < \infty$ and $w\in A_{p},$(i.e. the Muckenhoput weights), and establish weighted norm inequalities foroperators with rough and smooth amplitudes and phase functions satisfying asuitable rank condition. These results are then applied to prove weighted andunweighted estimates for the commutators of Fourier integral operators withfunctions of bounded mean oscillation BMO, then to some estimates on weightedTriebel-Lizorkin spaces, and finally to global unweighted and local weightedestimates for the solutions of the Cauchy problem for $m$-th and second orderhyperbolic partial differential equations on $\mathbf{R}^n .$

Global and local regularity of Fourier integral operators on weighted and unweighted spaces