Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Subordinated Bessel heat kernels

Krzysztof Bogdan, Konstantin Merz

Abstract

We prove new bounds for Bessel heat kernels and Bessel heat kernels subordinated by stable subordinators. In particular, we provide a 3G inequality in the subordinated case.

Subordinated Bessel heat kernels

Abstract

We prove new bounds for Bessel heat kernels and Bessel heat kernels subordinated by stable subordinators. In particular, we provide a 3G inequality in the subordinated case.
Paper Structure (11 sections, 5 theorems, 58 equations)

This paper contains 11 sections, 5 theorems, 58 equations.

Table of Contents

  1. Introduction and main result
  2. Fundamental properties, bounds, and explicit expressions
  3. 3G inequality for $\alpha\in(0,2)$
  4. Comparability results for $p_\zeta^{(\alpha)}$
  5. Proof of Theorem \ref{['heatkernelalpha1subordinatedboundsfinal']} for $\alpha\in(0,2)$
  6. Auxiliary bounds
  7. Case $rs\vee(r-s)^2<1$
  8. Case $(r-s)^2<1<rs$
  9. Case $rs<1<(r-s)^2$
  10. Case $rs\wedge(r-s)^2>1$
  11. Proof of \ref{['eq:heatkernelalpha1weightedsubordinatedboundsfinal']}

Key Result

Theorem 2.1

Let $\zeta\in(-1/2,\infty)$. Then, there are $c,c'>0$ such that for all $r,s,t>0$. Moreover, for all $\alpha\in(0,2)$ and all $r,s,t>0$,

Theorems & Definitions (10)

  • Theorem 2.1
  • proof : Proof of Theorem \ref{['heatkernelalpha1subordinatedboundsfinal']}
  • Proposition 2.2
  • proof
  • Theorem 3.1
  • proof : Proof of Theorem \ref{['3gheatalpha']}
  • Theorem 3.3: Bogdanetal2024
  • proof
  • Theorem 4.1
  • proof