منابع مشابه
Differential inequalities for Riesz means and Weyl-type bounds for eigenvalues
We derive differential inequalities and difference inequalities for Riesz means of eigenvalues of the Dirichlet Laplacian, Rσ(z) := ∑ k (z − λk) σ +. Here {λk} ∞ k=1 are the ordered eigenvalues of the Laplacian on a bounded domain Ω ⊂ Rd, and x+ := max(0, x) denotes the positive part of the quantity x. As corollaries of these inequalities, we derive Weyl-type bounds on λk, on averages such as λ...
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In R2, we consider an analytic family of fractional integrals , whose convolution kernel is obtained by taking some transverse derivatives of arclength measure on the parabola (t, t2) multiplied by |t|γ , and doing so in a homogeneous way. We determine the exact range of p, q for which the analytic family maps Lp to Lq . We also resolve a similar issue on the Heisenberg group.
متن کامل. SP ] 2 4 M ay 2 00 7 Differential inequalities for Riesz means and Weyl - type bounds for eigenvalues 1
We derive differential inequalities and difference inequalities for Riesz means of eigenvalues of the Dirichlet Laplacian, Rσ(z) := ∑ k (z − λk) σ +. Here {λk} ∞ k=1 are the ordered eigenvalues of the Laplacian on a bounded domain Ω ⊂ Rd, and x+ := max(0, x) denotes the positive part of the quantity x. As corollaries of these inequalities, we derive Weyl-type bounds on λk, on averages such as λ...
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In this note we improve the known L p-bounds for Bochner-Riesz operators and their maximal operators.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1996
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-96-03371-0