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      An affirmative answer to a conjecture of Honghai Liu concerning a λ-jump inequality on Hp spaces

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          Abstract

          Let ϕS with ϕ(x)dx=1, and define ϕt(x)=1tnϕ(xt),

          and denote the function family {ϕtf(x)}t>0 by Φf(x). Suppose that there exists a constant C1 such that t>0|ˆϕt(x)|2<C1
          for all xRn. Then the λ-jump operator Nλ(Φf) satisfies λ[Nλ(Φf)]1/2LpC2fHp,nn+1<p1,
          uniformly in λ>0 for some constant C2>0.

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          Author and article information

          Journal
          25 March 2022
          Article
          2203.13905
          630263b1-5a29-4f16-b44e-0a904459e18f

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Custom metadata
          42B25, 42B30
          math.CA

          Mathematics
          Mathematics

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