As for the positivity of 1 F 2 generalized hypergeometric functions, we present a list of necessary and sufficient conditions in terms of parameters and determine the region of positivity by certain Newton diagram.
Abstract. As a natural extension of L p Sobolev spaces, we consider Hardy-Sobolev spaces and establish an atomic decomposition theorem, analogous to the atomic decomposition characterization of Hardy spaces. As an application, we deduce several embedding results for Hardy-Sobolev spaces.
We present a rational extension of Newton diagram for the positivity of 1 F 2 generalized hypergeometric functions. As an application, we give upper and lower bounds for the transcendental roots β(α) ofwhere j α,2 denotes the second positive zero of Bessel function J α .
We characterize probability measure with finite moment of any order in terms of the symmetric difference operators of their Fourier transforms. By using our new characterization, we prove the continuitystands for the density of unique measure-valued solution (F t ) t≥0 of the Cauchy problem for the homogeneous non-cutoff Boltzmann equation, with Maxwellian molecules, corresponding to a probability measure initial datum F 0 satisfying |v| 2k−2+α dF 0 (v) < ∞, 0 ≤ α < 2, k = 2, 3, 4, · · · , provided that F 0 is not a single Dirac mass.MSC: Primary 35Q20, 76P05; secondary 35H20, 82B40, 82C40
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