Abstract
For 0 ≤α < ∞ let Tαf denote one of the operators
We characterize the pairs of weights (u, v) for which Tα is a bounded operator from Lp(v) to Lq(u), 0 <p ≤q < ∞. This extends to α > 0 the norm inequalities for α=0 in [4, 16]. As an application we give lower bounds for convolutions ϕ ⋆ f, where ϕ is a radially decreasing function.
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Communicated by Robert Strichartz
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Cruz-Uribe, D., Neugebauer, C.J. & Olesen, V. Weighted norm inequalities for geometric fractional maximal operators. The Journal of Fourier Analysis and Applications 5, 45–66 (1999). https://doi.org/10.1007/BF01274188
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DOI: https://doi.org/10.1007/BF01274188