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Two-weight norm inequalities for the Cesàro means of Hermite expansions |
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| Authors: | Benjamin Muckenhoupt David W. Webb |
| Affiliation: | Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019 ; Department of Mathematics, DePaul University, Chicago, Illinois 60614-7807 |
| Abstract: | An accurate estimate is obtained of the Cesàro kernel for Hermite expansions. This is used to prove two-weight norm inequalities for Cesàro means of Hermite polynomial series and for the supremum of these means. These extend known norm inequalities, even in the single power weight and ``unweighted' cases. An almost everywhere convergence result is obtained as a corollary. It is also shown that the conditions used to prove norm boundedness of the means and most of the conditions used to prove the boundedness of the Cesàro supremum of the means are necessary. |
| Keywords: | Ces`{a}ro means Hermite expansions Hermite polynomials two-weight norm inequalities weighted norm inequalities |
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