The higher order Riesz transform for Gaussian measure need not be of weak type (1, 1)

Studia Mathematica

Volumn 131, Issue 3, 1998, Pages 205-214

  Forzani, Liliana ^a   Scotto, Roberto ^b,c  

^a UNIVERSITY OF MINNESOTA   (United States)

^b UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

^c UNIVERSIDAD NACIONAL DE SALTA   (Argentina)

Author keywords

Fourier analysis; Gaussian measure; Hermite expansions; Poisson Hermite integrals

Indexed keywords

EID: 0001447374     PISSN: 00393223     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (7)

1. E. Fabes, C. Gutiérrez and R. Scotto, Weak-type estimates for the Riesz transforms associated with the Gaussian measure, Rev. Mat. Iberoamericana 10 (1994), 229-281.
2. C. Gutiérrez, On the Riesz transforms for the Gaussian measure, J. Funct. Anal. 120 (1994), 107-134.
3. C. Gutiérrez, C. Segovia and J. L. Torrea, On higher Riesz transforms for Gaussian measures, J. Fourier Anal. Appl. 2 (1996), 583-596.
4. B. Muckenhoupt, Hermite conjugate expansions, Trans. Amer. Math. Soc. 139 (1969), 243-260.
5. R. Scotto, Weak type stimates for singular integral operators associated with the Ornstein-Uhlenbeck process, PhD thesis, University of Minnesota.
6. P. Sjögren, On the maximal functions for the Mehler kernel, in: Lecture Notes in Math. 992, Springer, 1983, 73-82.
7. W. Urbina, On singular integrals with respect to the Gaussian measure, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 17 (1990), 531-567.