On properties of generalized quadratic operators
β Scribed by Chun Yuan Deng
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 161 KB
- Volume
- 432
- Category
- Article
- ISSN
- 0024-3795
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π SIMILAR VOLUMES
We consider the generalized Schro dinger operator &2++, where + is a nonnegative Radon measure in R n , n 3. Assuming that + satisfies certain scale-invariant Kato conditions and doubling conditions we establish the following bounds for the fundamental solution of &2++ in R n , where d(x, y, +) is
We show that if 0p -Ο± then the operator Gf s H f z dr 1 y z β«Ε½ . p p Ε½ < <. maps the Hardy space H to L d if and only if is a Carleson measure. Ε½ . Here β« is the usual nontangential approach region with vertex on the unit and d is arclength measure on the circle. We also show that if 0p F 1, β€ ) 0
For an integer k β₯ 2, k th -order slant Toeplitz operator UΟ [1] with symbol Ο in L β (T), where T is the unit circle in the complex plane, is an operator whose representing matrix M = (Ξ±ij ) is given by Ξ±ij = Ο, z ki-j , where . , . is the usual inner product in L 2 (T). The operator VΟ denotes the