Geodesic
Estimates with global range for oscillatory integrals with concave phase
Bjorn Gabriel Walther1
1 Royal Institute of Technology SE-100 44 Stockholm, Sweden and Brown University Providence, RI 02912-1917 U.S.A.
Colloquium Mathematicum, Tome 91 (2002) no. 2, pp. 157-165

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We consider the maximal function $\|(S^af)[x]\|_{L^\infty[-1,1]}$ where $(S^af) (t)^\wedge (\xi) = e ^ {i t |\xi| ^ a} \widehat f(\xi)$ and $0 a 1$. We prove the global estimate $$ \| {S ^ a f}\|_ {L ^ 2 (\mathbb R , L ^ \infty [ -1 , 1 ])} \leq C \| f \| _{H^ s(\mathbb R)}, \quad\ s > a/4, $$ with $C$ independent of $f$. This is known to be almost sharp with respect to the Sobolev regularity $s$.
DOI : 10.4064/cm91-2-1
Keywords: consider maximal function infty where wedge widehat prove global estimate mathbb infty leq mathbb quad independent known almost sharp respect sobolev regularity

Bjorn Gabriel Walther 1

1 Royal Institute of Technology SE-100 44 Stockholm, Sweden and Brown University Providence, RI 02912-1917 U.S.A. 
@article{10_4064_cm91_2_1,
     author = {Bjorn Gabriel Walther},
     title = {Estimates with global range for
oscillatory integrals with concave phase},
     journal = {Colloquium Mathematicum},
     pages = {157--165},
     publisher = {mathdoc},
     volume = {91},
     number = {2},
     year = {2002},
     doi = {10.4064/cm91-2-1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm91-2-1/}
}
TY  - JOUR
AU  - Bjorn Gabriel Walther
TI  - Estimates with global range for
oscillatory integrals with concave phase
JO  - Colloquium Mathematicum
PY  - 2002
SP  - 157
EP  - 165
VL  - 91
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm91-2-1/
DO  - 10.4064/cm91-2-1
LA  - en
ID  - 10_4064_cm91_2_1
ER  - 
%0 Journal Article
%A Bjorn Gabriel Walther
%T Estimates with global range for
oscillatory integrals with concave phase
%J Colloquium Mathematicum
%D 2002
%P 157-165
%V 91
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm91-2-1/
%R 10.4064/cm91-2-1
%G en
%F 10_4064_cm91_2_1
Bjorn Gabriel Walther. Estimates with global range for
oscillatory integrals with concave phase. Colloquium Mathematicum, Tome 91 (2002) no. 2, pp. 157-165. doi: 10.4064/cm91-2-1

Cité par Sources :