Author:
Author:
Tomasz Szarek
Tomasz Szarek
ul. W. Rutkiewicz 29/43, PL-50–571 Wrocław, Poland
Search for other papers by Tomasz Szarek in
Current site
Google Scholar
PubMed
Search for other papers by Tomasz Szarek in
Current site
Google Scholar
PubMed
Abstract
We investigate g-functions based on semigroups related to multi-dimensional Laguerre function expansions of convolution type. We prove that these operators can be viewed as Calderón–Zygmund operators in the sense of the underlying space of homogeneous type, hence their mapping properties follow from the general theory.
ProCite
RefWorks
Reference Manager
BibTeX
Zotero
EndNote
-
[1] Betancor, J. J., Fariña, J. C., Rodríguez-Mesa, L., Sanabria, A. and Torrea, J. L., Martingale type and cotype for Laguerre g-functions, Israel J. Math., to appear.
-
[2] Betancor, J. J., Fariña, J. C., Sanabria, A. 2009 On Littlewood–Paley functions associated with Bessel operators Glasgow Math. J. 51 55–70 .
-
[3] Betancor, J. J., Harboure, E., Nowak, A., Viviani, B. 2010 Mapping properties of fundamental operators in harmonic analysis related to Bessel operators Studia Math. 197 101–140 .
-
[4] Betancor, J. J., Molina, S. M. and Rodríguez-Mesa, L., Area Littlewood–Paley functions associated with Hermite and Laguerre operators, Potential Anal., to appear.
-
[5] Buraczewski, D., Martínez, T., Torrea, J. L. 2007 Calderón–Zygmund operators associated to ultraspherical expansions Canad. J. Math. 59 1223–1244 .
-
[6] Ciaurri, Ó., Roncal, L. 2010 Littlewood–Paley–Stein gk-functions for Fourier–Bessel expansions J. Funct. Anal. 258 2173–2204 .
-
[7] Coifman, R. R., Weiss, G. 1971 Analyse harmonique non-commutative sur certains espaces homogènes Lecture Notes in Mathematics 242 Springer Berlin–New York.
-
[8] Coifman, R. R., Rochberg, R., Weiss, G. 1978 Applications of transference: The Lp version of von Neumann’s inequality and Littlewood–Paley–Stein theory Linear Spaces and Approximation Birkhäuser Basel 53–67.
-
[9] Garrigós, G., Harboure, E., Signes, T., Torrea, J. L., Viviani, B. 2007 A sharp weighted transplantation theorem for Laguerre function expansions J. Funct. Anal. 244 247–276 .
-
[10] Gutiérrez, C. E., Incognito, A., Torrea, J. L. 2001 Riesz transforms, g-functions, and multipliers for the Laguerre semigroup Houston J. Math. 27 579–592.
-
[11] Harboure, E., Rosa de, L., Segovia, C., Torrea, J. L. 2004 Lp-dimension free boundedness for Riesz transforms associated to Hermite functions Math. Ann. 328 653–682 .
-
[12] Lebedev, N. N. 1972 Special Functions and Their Applications Dover New York.
-
[13] Meda, S. 1990 A general multiplier theorem Proc. Amer. Math. Soc. 110 639–647 .
-
[14] Nowak, A. 2003 Heat-diffusion and Poisson integrals for Laguerre and special Hermite expansions on weighted Lp spaces Studia Math. 158 239–268 .
-
[15] Nowak, A. 2004 On Riesz transforms for Laguerre expansions J. Funct. Anal. 215 217–240 .
-
[16] Nowak, A., Sjögren, P. 2008 Riesz transforms for Jacobi expansions J. Anal. Math. 104 341–369 .
-
[17] Nowak, A., Stempak, K. 2006 L2-theory of Riesz transforms for orthogonal expansions J. Fourier Anal. Appl. 12 675–711 .
-
[18] Nowak, A., Stempak, K. 2007 Riesz transforms for multi-dimensional Laguerre function expansions Adv. Math. 215 642–678 .
-
[19] Nowak, A., Stempak, K. 2009 Riesz transforms for the Dunkl harmonic oscillator Math. Z. 262 539–556 .
-
[20] Nowak, A. and Stempak, K., Imaginary powers of the Dunkl harmonic oscillator, Symmetry, Integrability and Geometry: Methods and Applications; SIGMA, 5 (2009), 016, 12 pages.
-
[21] Sasso, E. 2005 Functional calculus for the Laguerre operator Math. Z. 249 683 .
-
[22] Stein, E. M. 1970 Singular Integrals and Differentiability Properties of Functions Princeton Univ. Press Princeton, NJ.
-
[23] Stein, E. M. 1970 Topics in harmonic analysis related to the Littlewood–Paley theory Ann. Math. Stud. 63 1–146.
-
[24] Stein, E. M. 1982 The development of square functions in the work of A. Zygmund Bull. Amer. Math. Soc. 7 359–376 .
-
[25] Stein, E. M. 1993 Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory Integrals Princeton Univ. Press Princeton.
-
[26] Stempak, K. 1994 Heat-diffusion and Poisson integrals for Laguerre expansions Tôhoku Math. J. 46 83–104 .
-
[27] Stempak, K., Torrea, J. L. 2003 Poisson integrals and Riesz transforms for Hermite function expansions with weights J. Funct. Anal. 202 443–472 .
-
[28] Stempak, K., Torrea, J. L. 2005 On g-functions for Hermite function expansions Acta Math. Hungar. 109 99–125 .
-
[29] Stempak, K., Trebels, W. 1994 On weighted transplantation and multipliers for Laguerre expansions Math. Ann. 300 203–219 .
-
[30] Thangavelu, S. 1993 Lectures on Hermite and Laguerre Expansions Math. Notes 42 Princeton Univ. Press Princeton.
To see the editorial board, please visit the website of Springer Nature.
Manuscript Submission: HERE
For subscription options, please visit the website of Springer Nature.
| Acta Mathematica Hungarica | |
|---|---|
| Language | English |
| Size | B5 |
| Year of Foundation |
1950 |
| Volumes per Year |
3 |
| Issues per Year |
6 |
| Founder | Magyar Tudományos Akadémia  |
| Founder's Address |
H-1051 Budapest, Hungary, Széchenyi István tér 9. |
| Publisher | Akadémiai Kiadó Springer Nature Switzerland AG |
| Publisher's Address |
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245. CH-6330 Cham, Switzerland Gewerbestrasse 11. |
| Responsible Publisher |
Chief Executive Officer, Akadémiai Kiadó |
| ISSN | 0236-5294 (Print) |
| ISSN | 1588-2632 (Online) |
Monthly Content Usage
| Abstract Views | Full Text Views | PDF Downloads | |
|---|---|---|---|
| Aug 2024 | 4 | 0 | 0 |
| Sep 2024 | 13 | 0 | 0 |
| Oct 2024 | 11 | 0 | 0 |
| Nov 2024 | 15 | 0 | 0 |
| Dec 2024 | 14 | 0 | 0 |
| Jan 2025 | 2 | 0 | 0 |
| Feb 2025 | 0 | 0 | 0 |
Copyright Akadémiai Kiadó AKJournals is the trademark of Akadémiai Kiadó's journal publishing business branch.
Powered by PubFactory