Strichartz Estimates for Second Order Hyperbolic Operators with Nonsmooth Coefficients Iii
نویسنده
چکیده
Denote by x = (x0, x1, ..., xn) = (x0, x′) the coordinates in R × R. Sometimes we refer to the first coordinate x0 as “time” and to x′ as “space” coordinates. The Strichartz estimates for solutions to the homogeneous wave equation in R× R, 2u = 0, u(0) = u0, ut(0) = u1, have the form ‖|D|u‖Lp(Lq) . ‖∇u0‖L2 + ‖u1‖L2. (1.1) Such an estimate holds for all pairs (ρ, p, q) satisfying the relations 2 ≤ p ≤ ∞, 2 ≤ q ≤ ∞ and 1 p + n q = n 2 − ρ, 2 p + n− 1 q ≤ n− 1 2 (1.2)
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