Abstract
We study two-weight norm inequality for imaginary powers of a Laplace operator in \({\boldmath{R}}^{n}, n\geq 1\), especially from weighted Lebesgue space \(L^p_\nu({\boldmath{R}}^{n})\) to weighted Lebesgue space \(L^p_\mu({\boldmath{R}}^{n})\), where \(1<p<\infty\). We prove that the two-weighted norm inequality holds whenever for some \(t>1, (\mu^{t},\nu^{t})\in A_p\), or if \((\mu,\nu)\in A_p\), where \(\mu\) and \(\nu^{-{{1}\over{p-1}}}\) satisfy the growth condition and reverse doubling property.
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Zhang, J. Two-Weight Norm Inequality for Imaginary Powers of a Laplace Operator. Jrl Syst Sci & Complex 19, 403–408 (2006). https://doi.org/10.1007/s11424-006-0403-y
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DOI: https://doi.org/10.1007/s11424-006-0403-y