Variable exponent Fock spaces

Gerardo R. Chacón; Gerardo A. Chacón

Czechoslovak Mathematical Journal (2020)

  • Volume: 70, Issue: 1, page 187-204
  • ISSN: 0011-4642

Abstract

top
We introduce variable exponent Fock spaces and study some of their basic properties such as boundedness of evaluation functionals, density of polynomials, boundedness of a Bergman-type projection and duality. We also prove that under the global log-Hölder condition, the variable exponent Fock spaces coincide with the classical ones.

How to cite

top

Chacón, Gerardo R., and Chacón, Gerardo A.. "Variable exponent Fock spaces." Czechoslovak Mathematical Journal 70.1 (2020): 187-204. <http://eudml.org/doc/297045>.

@article{Chacón2020,
abstract = {We introduce variable exponent Fock spaces and study some of their basic properties such as boundedness of evaluation functionals, density of polynomials, boundedness of a Bergman-type projection and duality. We also prove that under the global log-Hölder condition, the variable exponent Fock spaces coincide with the classical ones.},
author = {Chacón, Gerardo R., Chacón, Gerardo A.},
journal = {Czechoslovak Mathematical Journal},
keywords = {Fock space; variable exponent Lebesgue space; Bergman projection},
language = {eng},
number = {1},
pages = {187-204},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Variable exponent Fock spaces},
url = {http://eudml.org/doc/297045},
volume = {70},
year = {2020},
}

TY - JOUR
AU - Chacón, Gerardo R.
AU - Chacón, Gerardo A.
TI - Variable exponent Fock spaces
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 1
SP - 187
EP - 204
AB - We introduce variable exponent Fock spaces and study some of their basic properties such as boundedness of evaluation functionals, density of polynomials, boundedness of a Bergman-type projection and duality. We also prove that under the global log-Hölder condition, the variable exponent Fock spaces coincide with the classical ones.
LA - eng
KW - Fock space; variable exponent Lebesgue space; Bergman projection
UR - http://eudml.org/doc/297045
ER -

References

top
  1. Chacón, G. R., Rafeiro, H., 10.1016/j.na.2014.04.001, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 105 (2014), 41-49. (2014) Zbl1288.30059MR3200739DOI10.1016/j.na.2014.04.001
  2. Chacón, G. R., Rafeiro, H., 10.1007/s00009-016-0701-0, Mediterr. J. Math. 13 (2016), 3525-3536. (2016) Zbl1354.30049MR3554324DOI10.1007/s00009-016-0701-0
  3. Chacón, G. R., Rafeiro, H., Vallejo, J. C., 10.1007/s11785-016-0573-0, Complex Anal. Oper. Theory 11 (2017), 1623-1638. (2017) Zbl1387.30081MR3702967DOI10.1007/s11785-016-0573-0
  4. Cruz-Uribe, D. V., Fiorenza, A., 10.1007/978-3-0348-0548-3, Applied and Numerical Harmonic Analysis, Birkhäuser, Basel (2013). (2013) Zbl1268.46002MR3026953DOI10.1007/978-3-0348-0548-3
  5. Diening, L., Harjulehto, P., Hästö, P., Růžička, M., 10.1007/978-3-642-18363-8, Lecture Notes in Mathematics 2017, Springer, Berlin (2011). (2011) Zbl1222.46002MR2790542DOI10.1007/978-3-642-18363-8
  6. Harjulehto, P., Hästö, P., Klén, R., 10.1016/j.na.2016.05.002, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 143 (2016), 155-173. (2016) Zbl1360.46029MR3516828DOI10.1016/j.na.2016.05.002
  7. Isralowitz, J., 10.7900/jot.2012apr10.1989, J. Oper. Theory 71 (2014), 381-410. (2014) Zbl1313.47059MR3214643DOI10.7900/jot.2012apr10.1989
  8. Karapetyants, A., Samko, S., 10.1515/GMJ.2010.028, Georgian Math. J. 17 (2010), 529-542. (2010) Zbl1201.30072MR2719633DOI10.1515/GMJ.2010.028
  9. Karapetyants, A. N., Samko, S. G., 10.1134/S000143461607004X, Math. Notes 100 (2016), 38-48 translation from Mat. Zametki 100 2016 47-58. (2016) Zbl1364.30063MR3588827DOI10.1134/S000143461607004X
  10. Karapetyants, A. N., Samko, S. G., 10.1080/17476933.2016.1140750, Complex Var. Elliptic Equ. 61 (2016), 1090-1106. (2016) Zbl1351.30042MR3500518DOI10.1080/17476933.2016.1140750
  11. Kokilashvili, V., Paatashvili, V., On Hardy classes of analytic functions with a variable exponent, Proc. A. Razmadze Math. Inst. 142 (2006), 134-137. (2006) Zbl1126.47031MR2294576
  12. Kokilashvili, V., Paatashvili, V., On the convergence of sequences of functions in Hardy classes with a variable exponent, Proc. A. Razmadze Math. Inst. 146 (2008), 124-126. (2008) Zbl1166.47033MR2464049
  13. Kováčik, O., Rákosník, J., 10.21136/CMJ.1991.102493, Czech. Math. J. 41 (1991), 592-618. (1991) Zbl0784.46029MR1134951DOI10.21136/CMJ.1991.102493
  14. Lefèvre, P., Li, D., Queffélec, H., Rodríguez-Piazza, L., 10.1090/S0065-9266-10-00580-6, Mem. Am. Math. Soc. 207 (2010), 74 pages. (2010) Zbl1200.47035MR2681410DOI10.1090/S0065-9266-10-00580-6
  15. Lefèvre, P., Li, D., Queffélec, H., Rodríguez-Piazza, L., 10.1090/S0002-9947-2013-05922-3, Trans. Am. Math. Soc. 365 (2013), 3943-3970. (2013) Zbl1282.47033MR3055685DOI10.1090/S0002-9947-2013-05922-3
  16. Motos, J., Planells, M. J., Talavera, C. F., 10.1016/j.jmaa.2011.09.069, J. Math. Anal. Appl. 388 (2012), 775-787. (2012) Zbl1244.46008MR2869787DOI10.1016/j.jmaa.2011.09.069
  17. Orlicz, W., 10.4064/sm-3-1-200-211, Stud. Math. 3 (1931), 200-211 German. (1931) Zbl0003.25203DOI10.4064/sm-3-1-200-211
  18. Tung, Y.-C. J., Fock Spaces, Ph.D. Thesis, The University of Michigan (2005). (2005) MR2706955
  19. Zhu, K., 10.1007/978-1-4419-8801-0, Graduate Texts in Mathematics 263, Springer, New York (2012). (2012) Zbl1262.30003MR2934601DOI10.1007/978-1-4419-8801-0

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.