On the Cowling-Price theorem for {$\rm SU(1,1)$}

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$C\epsilon^{-(J.\}}’ 2$ and $|.\hat{f}(y)|\leq Ce^{-by^{2}}$ and $ab> \frac{1}{4}$ then.f $=0(a.e.)$ . Here we use the Fourier transforlll defined $by.\hat{f}(y)=(1/\sqrt{2\pi})\int_{-(\infty}^{\iota\lambda^{\hat{\mathfrak{l}}}}f(x)e^{\sqrt{-1}x\cdot y}dx$ . M. G. Cowling and J. F. Price [3] generalized the Hardy theorem as follows: Suppose $tha,t1\leq p,$ $q\leq$ oo and one of thelll is finite. lf a lneasurable function. $f$ . on $R$ satisfies $||\exp\{ax^{2}\}.f(x)||_{L^{p}(R)}<\infty$ and