On the pointwise convergence to initial data of heat and Poisson problems for the Bessel operator

2015/05/13 by Isolda Cardoso, Cardoso, Isolda · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1505.03494

25 pages

arxiv created 2015/05/13 · arxiv updated 2015/05/14

Abstract

We find optimal integrability conditions on the initial data f for the existence of solutions e^-tΔ_λf(x) and e^-t√(Δ_λ)f(x) of the heat and Poisson initial data problems for the Bessel operator Δ_λ in ℝ⁺. We also characterize the most general class of weights v for which the solutions converge a.e. to f for every f∈ L^p(v), with 1≤ p<∞. Finally, we show that for such weights and 1<p<∞ the local maximal operators are bounded from L^p(v) to L^p(u), for some weight u.

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• Pointwise convergence to initial data of heat and Hermite-heat equations in Modulation Spaces

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