Bounds on the Phillips calculus of abstract first order differential\n operators

2020/12/17 by Himani Sharma, Sharma, Himani
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2012.10041

openalex publication_date 2020/12/17 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

For an operator generating a group on L^p spaces transference results give\nbounds on the Phillips functional calculus also known as spectral multiplier\nestimates. In this paper we consider specific group generators which are\nabstraction of first order differential operators and prove similar spectral\nmultiplier estimates assuming only that the group is bounded on L² rather\nthan L^p. We also prove an R-bounded H "ormander calculus result by assuming\nan abstract Sobolev embedding property and show that the square of a perturbed\nHodge-Dirac operator has such calculus.\n

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