- Tytuł:
- On the maximal operator associated with the free Schrödinger equation
- Autorzy:
- Wang, Sichun
- Powiązania:
- https://bibliotekanauki.pl/articles/1220332.pdf
- Data publikacji:
- 1997
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
free Schrödinger equation
maximal functions
spherical harmonics
oscillatory integrals - Opis:
- For d > 1, let $(S_{d}f)(x,t) = ʃ_{ℝ^n} e^{ix·ξ} e^{it|ξ|^d} f̂(ξ)dξ$, $x ∈ ℝ^n$, where f̂ is the Fourier transform of $f ∈ S (ℝ^n)$, and $(S_{d}*f)(x) = sup_{0 < t < 1} |(S_{d}f)(x,t)|$ its maximal operator. P. Sjölin ([11]) has shown that for radial f, the estimate (*) $(\int_{|x| < R} |(S_{d}*f)(x)|^p dx)^{1//p} ≤ C_{R}∥f∥_{H_{1//4}}$ holds for p = 4n//(2n-1) and fails for p > 4n/(2n-1). In this paper we show that for non-radial f, (*) fails for p > 2. A similar result is proved for a more general maximal operator.
- Źródło:
-
Studia Mathematica; 1997, 122, 2; 167-182
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł