On Dilations of Fourier Multipliers on Weighted Lebesgue Spaces

Karlovych, Oleksiy; Shargorodsky, Eugene

http://hdl.handle.net/10362/174179

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Autores

Karlovych, Oleksiy

Shargorodsky, Eugene

Resumo(s)

For a given p∈(1,∞), we present an example of a Muckenhoupt weight w∈Ap and a Fourier multiplier a on the weighted Lebesgue space Lp(w) such that, for any τ∈ℝ∖{0,1}, the dilation of a given by aτ(ξ)=a(τξ) is not a Fourier multiplier on Lp(w).