We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Boundedness of Stein's spherical maximal function in variable Lebesgue spaces and application to the wave equation.
- Authors
Fiorenza, Alberto; Gogatishvili, Amiran; Kopaliani, Tengiz
- Abstract
If $${p(\cdot): \mathbb{R}^{n} {\rightarrow} (0,\infty), n\geq 3}$$, is globally log-Hölder continuous and its infimum p and its supremum p are such that $${\frac{n}{n-1} < p^{-} \leq p^{+} < p^{-} (n-1)}$$, then the spherical maximal operator (integral averages taken with respect to the ( n − 1)-dimensional surface measure) is bounded. When n = 3, the result is then interpreted as the preservation of the integrability properties of the initial velocity of propagation to the solution of the initial-value problem for the wave equation.
- Publication
Archiv der Mathematik, 2013, Vol 100, Issue 5, p465
- ISSN
0003-889X
- Publication type
Article
- DOI
10.1007/s00013-013-0509-0