Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
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...These results extend a long line of investigation going back to a specific space-time estimate for the linear Klein-Gordon equation in [18] and the fundamental paper of Strichartz [24] drawing the connection to the restriction theorems of Tomas and Stein....
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"Restrictions of Fourier transforms ..." refers background or methods in this paper
...Thus u L(IR" + a) when rn > 0, the usual Sobolev space of Bessel potentials (see [7]), and u L(IR" + 1) when m 0, the homogeneous Sobolev space of Riesz potentials (say for 0 < s < n/q to avoid technicalities)....
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...Choose jy) (1 + [yl)<Thenf L provided ap < n 0ehas a singularity like ixl near zero and exponential decay at infinity; see [7])....
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...As an immediate application of Stein’s interpolation theorem (see [7]) we have LEMMA 2....
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"Restrictions of Fourier transforms ..." refers background in this paper
...Fefferman [3], and in this case the answer is known (see [l I])....
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270 citations
"Restrictions of Fourier transforms ..." refers background or methods in this paper
...fGz(x)p(x)dx= y(z)I( fs, pdlt)(t- r)z+dt so it follows from the one-dimensional analysis of (t r)%(see [4]) that...
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...The computation of (z is also given in Gelfand-Shilov [4] p....
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...The computation of (z is also given in Gelfand-Shilov [4] p. 290 (an alternate derivation may be given following a similar computation in 10] p. 516)....
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...Finally we want to point out that none of the methods used in this paper are new; even the computations in section 2 can be found in some form in [4]....
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...The computation of the Fourier transform may be found in Gelfand-Shilov [4], p....
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