Exact log growth exponents of L^p norms (1 to infinity) for disk eigenfunctions are determined, along with sharp uniform upper and lower bounds, via stationary phase and Bessel integral estimates.
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Proves an order-interpolation inequality for squares of Bessel functions of the first and second kinds and applies it to bound optimal constants for Schrödinger smoothing estimates across dimensions.
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Exact $L^p$ growth rates of Laplace eigenfunctions on the unit disk
Exact log growth exponents of L^p norms (1 to infinity) for disk eigenfunctions are determined, along with sharp uniform upper and lower bounds, via stationary phase and Bessel integral estimates.