The Hausdorff-Young inequality for n-dimensional Hermite expansions


  • Calixto P. Calderón Department of Math. Stat. & Comp Sci, University of Illinois at Chicago, Chicago IL 60607 USA
  • Alberto Torchinsky Department of Mathematics, Indiana University, Bloomington, Indiana 47405, USA.



Hausdorff-Young inequality, , n-dimensional Hermite expansions


We discuss a sharpened Hausdorff–Young inequality for n-dimensional Hermite expansions.


Bennett C and Sharpley R. Interpolation of Operators, Academic Press, Orlando, Florida, 1988.

Butzer PL. The Hausdorff–Young theorems of Fourier analysis and their impact, J. Fourier Anal. Appl. 1994; (1):113--130.

Calderón AP. Spaces between L^1 and L^infty and the theorem of Marcinkiewicz, Studia Math. XXVI. 1966; 273--299.

Calderón CP and Torchinsky A. Maximal integral inequalities and Hausdorff--Young, preprint.

Hille E. A class of reciprocal functions, Ann. of Math. 1926; (2): 27(4):427-464.

Hunt RA. On L(p, q) spaces, Enseign. Math. 1966; 12(2):249--276.

Jodeit M Jr. and Torchinsky A. Inequalities for Fourier transforms, Studia Math. XXXVII. 1971; 245--276.

Krasnosels'kii MA and Rutickii Ya B. Convex functions and Orlicz spaces, Nordhoff, Groningen, 1961.

Oklander ET. Interpolaci'on, Espacios de Lorentz, y el Teorema de Marcinkiewicz, Cursos y Seminarios 20, U. de Buenos Aires, 1965.

Pinsky MA and Prather C. Pointwise convergence of n--dimensional Hermite expansions, Jour. Math. Anal. and Appl. 1996; 199:620-628.

Stein EM and Weiss G. Introduction to Fourier Analysis on Euclidean Spaces, Princeton Mathematical Series, Princeton University Press, Princeton, NJ, 1971.

Szegö G. Orthogonal polynomials, rev. ed., Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc, Providence, R. I., 1959.

Torchinsky A. Interpolation of operations and Orlicz classes , Studia Math. LIX. 1976/77; 2:177--207.

Urbina--Romero W. Gaussian Harmonic Analysis}, {Springer International Publishing, 2019.

Zygmund A. Trigonometric Series. Vol. I, II, 3rd edition, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 2002.




How to Cite

P. Calderón , C., & Torchinsky, A. (2022). The Hausdorff-Young inequality for n-dimensional Hermite expansions. Selecciones Matemáticas, 9(02), 227 - 233.