Article PDF
Avoid common mistakes on your manuscript.
References
Calderón, A. P., Intermediate spaces and interpolation, the complex method,Studia Math. 24 (1964), 113–190.
Carleson &Sjölin, P., Oscillatory integrals and a multiplier problem for the disc,Studia Math. 44 (1972), 287–299.
Coifman, R. R. &Weiss, G., Extensions of Hardy spaces and their use in Analysis,Bull. Amer. Math. Soc. 83 (1977), 569–645.
Drobot, V., Naparstek, A., &Sampson, G., (L p ,L q ) mapping properties of convolution transforms,Studia Math. 55 (1976), 41–70.
Fefferman, C., Inequalities for strongly singular convolution operators,Acta Math. 124 (1970), 9–36.
Fefferman, C. &Stein, E. M.,H p spaces of several variables,Acta Math. 129 (1972), 137–193.
Hörmander, L. Oscillatory integrals and multipliers onFL p,Ark. Mat. 11 (1973), 1–11.
Jurkat, W. B. &Sampson, G., TheL p mapping problem for well-behaved convolutions,Studia Math. 65 (1978), 1–12.
Jurkat, W. B. & Sampson, G., The (L p,L q) mapping problem for oscillating kernels.
Jurkat, W. B. & Sampson, G., On weak restricted estimates and end point problems for convolutions with oscillating kernels (I), submitted for publication.
Jurkat, W. B. & Sampson, G. The complete solution to the (L p,L q) mapping problem for a class of oscillating kernels.
Macias, R.,H p-space interpolation theorems, Ph. D. Thesis, Washington Univ., St. Louis, Mo., 1975.
Peral, J. C. andTorchinsky, A., Multipliers inH p(R n), 0<p<∞, preprint.
Sampson, G., A note on weak estimates for oscillatory kernels,Studia Math. (to appear).
Sampson, G., More on weak estimates of oscillatory kernels,Indiana Univ. Math. J. 28 (1979), 501–505.
Sampson, G., More on weak estimates of oscillatory kernels (II),Indiana Univ. Math. J. (to appear).
Sjölin, P., Convergence a.e. of certain singular integrals and multiple Fourier series,Ark. Mat. 9 (1971), 65–90.
Sjölin, P.,L p estimates for strongly singular convolution operators inR n Ark. Mat. 14 (1976), 59–94.
Sjölin, P., Convolution with oscillating kernels, preprint.
Zafran, M., Multiplier transformations of weak type,Ann. of Math. (2),101 (1975), 34–44.
Zygmund, A.,Trigonometric Series, 2 nd ed., Vols. 1 and 2, Cambridge Univ. Press, New York, 1959.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sampson, G. Oscillating kernels that mapH 1 intoL 1 . Ark. Mat. 18, 125–144 (1980). https://doi.org/10.1007/BF02384686
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02384686