Boundedness of differential transforms for Poisson semigroups generated by Bessel operators

2022/04/08 by Zhang, Chao
#42B20 #42B25 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2204.04265

Abstract

In this paper we analyze the convergence of the following type of series T_N f(x)=∑_j=N1^N₂ v_j(P_a_j+1 f(x)-P_a_j f(x)), x∈ \mathbb R₊, where \P_t \_t>0 is the Poisson semigroup of the Bessel operator Δ_λ:=-d²\over dx²-2λ\over xd\over dx with λ being a positive constant, N=(N₁, N₂)∈ \mathbb Z² with N₁

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