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Let p and q be conjugate exponents, with p in [1,2]. It is shown that theLaplace transform acts boundedly between the Lp space with unit weight on thepositive real semiaxis and the Lq space weighted by a well-projected measure (aterm defined in the paper) in the right complex half-plane. The operator normis uniformly bounded over classes of measures with the same "projectionconstants". Particular cases are arclength measures on some classes ofrectifiable curves. In addition, an analog of the Hausdorff-Young inequality inLorentz spaces is obtained in the case of "wrong" exponents p>2.

Hausdorff-Young type theorems for the Laplace transform restricted to a ray or to a curve in the complex plane