Boundedness of differential transforms for heat semigroups generated by fractional Laplacian

2021/11/01 by Ren, Xinyu, Zhang, Chao
#42B20 #42B25 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2111.00725

Abstract

In this paper we analyze the convergence of the following type of series T_N f(x)=∑_j=N1^N₂ v_j(e^-a_j+1(-Δ)^α f(x)-e^-a_j(-Δ)^α f(x)), x∈ \mathbb Rⁿ, where \e^-t(-Δ)α \_t>0 is the heat semigroup of the fractional Laplacian (-Δ)^α, N=(N₁, N₂)∈ \mathbb Z² with N₁

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