The Multi-Dimensional Pencil Phenomenon for Laguerre Heat-Diffusion Maximal Operators
Journal article, 2009

We investigate in detail the mapping properties of the maximal operator associated with the heat-diffusion semigroup corresponding to expansions with respect to multi-dimensional standard Laguerre functions $${mathcal{L}^{alpha}_k}$$ . Our interest is focused on the situation when at least one coordinate of the type multi-index α is smaller than 0. For such parameters α the Laguerre semigroup does not satisfy the general theory of semigroups, and the behavior of the associated maximal operator on L p spaces is found to depend strongly on both α and the dimension.


Adam Nowak

Wrocław University of Science and Technology

Peter Sjögren

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Mathematische Annalen

0025-5831 (ISSN) 1432-1807 (eISSN)

Vol. 344 1 213-248

Subject Categories

Mathematical Analysis



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