In mathematical analysis, Strichartz estimates are a family of inequalities for linear dispersive partial differential equations. These inequalities establish size and decay of solutions in mixed norm Lebesgue spaces. They were first noted by Robert Strichartz and arose out of connections to the Fourier restriction problem.
Examples.
Consider the linear Schrödinger equation in formula_1 with "h" = "m" = 1. Then the solution for initial data formula_2 is given by formula_3. Let "q" and "r" be real numbers satisfying formula_4; formula_5; and formula_6. 
In this case the homogeneous Strichartz estimates take the form:
formula_7 
Further suppose that formula_8 satisfy the same restrictions as formula_9 and formula_10 are their dual exponents, then the dual homogeneous Strichartz estimates take the form:
formula_11
The inhomogeneous Strichartz estimates are:
formula_12
References.
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