English

On embedding of Besov spaces of zero smoothness into Lorentz spaces

Classical Analysis and ODEs 2023-01-18 v1 Functional Analysis

Abstract

We show that the zero smoothness Besov space Bp,q0,1B_{p,q}^{0,1} does not embed into the Lorentz space Lp,qL_{p,q} unless p=qp=q; here p,q(1,)p,q\in (1,\infty). This answers negatively a question proposed by O. V. Besov.

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Cite

@article{arxiv.2301.06370,
  title  = {On embedding of Besov spaces of zero smoothness into Lorentz spaces},
  author = {Dmitriy Stolyarov},
  journal= {arXiv preprint arXiv:2301.06370},
  year   = {2023}
}

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8 pages