Weighted L-2 estimates for maximal operators associated to dispersive equations
SCIE
SCOPUS
- Title
- Weighted L-2 estimates for maximal operators associated to dispersive equations
- Authors
- Cho, YG; Shim, YS
- Date Issued
- 2004-01
- Publisher
- UNIV ILLINOIS URBANA-CHAMPAIGN
- Abstract
- Let Tf (x, t) = e(2 pi it phi(D)) f(x) be the solution of the general dispersive equation with phase phi and initial data f in the Sobolev space H-s. We prove a weighted L-2 estimate for the global maximal operator T** defined by taking the supremum over the time variable t is an element of R so that vertical bar vertical bar T**f vertical bar vertical bar L-2(w dx) <= C vertical bar vertical bar f vertical bar vertical bar H-3. The exponent s depends on the phase function 0, whose gradient may vanish or have singularities.
- Keywords
- SCHRODINGER-EQUATION; OSCILLATORY INTEGRALS
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/29630
- DOI
- 10.1215/ijm/1258138500
- ISSN
- 0019-2082
- Article Type
- Article
- Citation
- ILLINOIS JOURNAL OF MATHEMATICS, vol. 48, no. 4, page. 1081 - 1092, 2004-01
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