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- W4239106384 abstract "We study the operator [ mathcal {H}f(x) = {2^{ - x}}int _0^{ + infty } {frac {{{2^y}f(y)}}{{x - y}}dy} ] on Lorentz spaces on ${mathbb {R}_ + }$ with respect to the measure ${4^x}dx$. This is related to the harmonic analysis of radial functions on hyperbolic spaces. We prove that this operator is bounded on the Lorentz spaces ${L^{2,9}}({mathbb {R}_ + },{4^x}dx),1 < q < + infty$, and it maps the Lorentz space ${L^{2,1}}({mathbb {R}_ + },{4^x}dx)$ into a space that we call WEAK-${L^{2,1}}({mathbb {R}_ + },{4^x}dx)$. We also prove that $mathcal {H}$ maps ${L^1}({mathbb {R}_ + },{4^x}dx)$ into WEAK-${L^1}({mathbb {R}_ + },{4^x}dx) + {L^2}({mathbb {R}_ + },{4^x}dx)$." @default.
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- W4239106384 date "1992-02-01" @default.
- W4239106384 modified "2023-10-14" @default.
- W4239106384 title "The Hilbert Transform with Exponential Weights" @default.
- W4239106384 doi "https://doi.org/10.2307/2159667" @default.
- W4239106384 hasPublicationYear "1992" @default.
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