<p>Assuming a weighted Nash type inequality for the generator <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(-A\)</EquationSource> </InlineEquation> of a Markov semigroup, we prove a weighted Nash type inequality for its fractional power and deduce non-uniform bounds on the transition kernel corresponding to the Markov semigroup generated by <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(-A^\alpha \)</EquationSource> </InlineEquation>.</p>

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Kernel estimates for a class of fractional Kolmogorov operators

  • Marianna Porfido,
  • Abdelaziz Rhandi,
  • Cristian Tacelli

摘要

Assuming a weighted Nash type inequality for the generator \(-A\) of a Markov semigroup, we prove a weighted Nash type inequality for its fractional power and deduce non-uniform bounds on the transition kernel corresponding to the Markov semigroup generated by \(-A^\alpha \) .