Establishes integrability conditions for heat solutions on the Heisenberg group, characterizes weighted spaces for a.e. convergence as t to 0, and shows boundedness of the local heat-kernel maximal function with weights.
Thangavelu, An Introduction to the Uncertainty Principle: Hardy’s Theo rem on Lie Groups , Progress in Mathematics (2012)
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About the convergence to initial data of the heat problem on the Heisenberg group
Establishes integrability conditions for heat solutions on the Heisenberg group, characterizes weighted spaces for a.e. convergence as t to 0, and shows boundedness of the local heat-kernel maximal function with weights.