Global $L^{2}$ estimates for a class of maximal operators associated to general dispersive equations

Journal of Inequalities and Applications

Table 2 Global $\pmb{L^{2}}$ estimate ( 1.4 ) for $\pmb{f\in H^{s}(\mathbb {R}^{n})}$

Dim.	Ran. of a	Ran. of s	Authors
n ≥ 1	a>0	$s>\frac{a}{2}$	Cowling [11] in 1983 and Carbery [12] in 1985, independently
n = 1	a ≥ 2	$s>\frac{a}{4}$	Kenig, Ponce and Vega [13] in 1991
n = 1	a>1	$s>\frac{a}{4}$	Sjölin [14] in 1994
n = 1	0<a<1	$s>\frac{a}{4}$	Walther [15] in 2002

Dim.	Ran. of a	Ran. of s	Authors
n ≥ 1	a>0	\(s>\frac{a}{2}\)	Cowling [11] in 1983 and Carbery [12] in 1985, independently
n = 1	a ≥ 2	\(s>\frac{a}{4}\)	Kenig, Ponce and Vega [13] in 1991
n = 1	a>1	\(s>\frac{a}{4}\)	Sjölin [14] in 1994
n = 1	0<a<1	\(s>\frac{a}{4}\)	Walther [15] in 2002