• Corpus ID: 119714608

$L^p$-$L^q$ multipliers on locally compact groups

@article{Akylzhanov2015LpLqMO,
  title={\$L^p\$-\$L^q\$ multipliers on locally compact groups},
  author={Rauan Akylzhanov and Michael Ruzhansky},
  journal={arXiv: Representation Theory},
  year={2015}
}
In this paper we discuss the $L^p$-$L^q$ boundedness of both spectral and Fourier multipliers on general locally compact separable unimodular groups $G$ for the range $1<p\leq q<\infty$. We prove a Lizorkin type multiplier theorem for $1<p\leq q<\infty$, and then refine it as a H\"ormander type multiplier theorem for $1<p\leq 2\leq q<\infty$. In the process, we establish versions of Paley and Hausdorff-Young-Paley inequalities on general locally compact separable unimodular groups. As a… 

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