{"paper":{"title":"$L^p$ Boundedness of rough Bi-parameter Fourier Integral Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Guozhen Lu, Lu Zhang, Qing Hong","submitted_at":"2015-10-04T21:15:23Z","abstract_excerpt":"In this paper, we will investigate the boundedness of the bi-parameter Fourier integral operators (or FIOs for short) of the following form: $$T(f)(x)=\\frac{1}{(2\\pi)^{2n}}\\int_{\\mathbb{R}^{2n}}e^{i\\varphi(x,\\xi,\\eta)}\\cdot a(x,\\xi,\\eta)\\cdot\\widehat{f}(\\xi,\\eta)d\\xi d\\eta,$$ where for $x=(x_1,x_2)\\in \\mathbb{R}^{n}\\times \\mathbb{R}^{n}$ and $\\xi,\\eta \\in \\mathbb{R}^{n}\\setminus\\{0\\}$, the amplitude $a(x,\\xi,\\eta)\\in L^\\infty BS^m_\\rho$ and the phase function is of the form $\n\\varphi(x,\\xi,\\eta)=\\varphi_1(x_1,\\xi)+\\varphi_2(x_2,\\eta)$ with $\\quad \\varphi_1,\\varphi_2 \\in L^\\infty \\Phi^2 (\\mathb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00986","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}