On some inequalities in holomorphic function theory in polydisk related to diagonal mapping

Romi F. Shamoyan; Olivera R. Mihić

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 2, page 351-370
  • ISSN: 0011-4642

Abstract

top
We present a description of the diagonal of several spaces in the polydisk. We also generalize some previously known contentions and obtain some new assertions on the diagonal map using maximal functions and vector valued embedding theorems, and integral representations based on finite Blaschke products. All our results were previously known in the unit disk.

How to cite

top

Shamoyan, Romi F., and Mihić, Olivera R.. "On some inequalities in holomorphic function theory in polydisk related to diagonal mapping." Czechoslovak Mathematical Journal 60.2 (2010): 351-370. <http://eudml.org/doc/38012>.

@article{Shamoyan2010,
abstract = {We present a description of the diagonal of several spaces in the polydisk. We also generalize some previously known contentions and obtain some new assertions on the diagonal map using maximal functions and vector valued embedding theorems, and integral representations based on finite Blaschke products. All our results were previously known in the unit disk.},
author = {Shamoyan, Romi F., Mihić, Olivera R.},
journal = {Czechoslovak Mathematical Journal},
keywords = {polydisk; diagonal mapping; Hardy classes; holomorphic spaces; diagonal mapping; Hardy class; holomorphic space},
language = {eng},
number = {2},
pages = {351-370},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On some inequalities in holomorphic function theory in polydisk related to diagonal mapping},
url = {http://eudml.org/doc/38012},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Shamoyan, Romi F.
AU - Mihić, Olivera R.
TI - On some inequalities in holomorphic function theory in polydisk related to diagonal mapping
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 2
SP - 351
EP - 370
AB - We present a description of the diagonal of several spaces in the polydisk. We also generalize some previously known contentions and obtain some new assertions on the diagonal map using maximal functions and vector valued embedding theorems, and integral representations based on finite Blaschke products. All our results were previously known in the unit disk.
LA - eng
KW - polydisk; diagonal mapping; Hardy classes; holomorphic spaces; diagonal mapping; Hardy class; holomorphic space
UR - http://eudml.org/doc/38012
ER -

References

top
  1. Aleksandrov, A. V., 10.1007/BFb0096996, Springer-Verlag, Complex Analysis and spectral theory V. V. Havin and N. K. Nikolski (1981), 1-99. (1981) MR0643380DOI10.1007/BFb0096996
  2. Amar, E., Menini, C., A counterexample to the corona theorem for operators on H 2 ( D n ) , Pacific J. Math. 206 (2002), 257-268. (2002) MR1926777
  3. Clark, D., 10.2307/2374688, Amer. J. Math. 110 (1988), 1119-1152. (1988) MR0970122DOI10.2307/2374688
  4. Coifman, R., Meyer, Y., Stein, E., 10.1016/0022-1236(85)90007-2, J. Funct. Anal. 62 (1985), 304-335. (1985) MR0791851DOI10.1016/0022-1236(85)90007-2
  5. Djrbashian, A. E., Shamoyan, F. A., Topics in the Theory of A α p Spaces, Leipzig, Teubner (1988). (1988) Zbl0667.30032MR1021691
  6. Duren, P. L., Shields, A. L., 10.1215/S0012-7094-75-04262-3, Duke Math. J. 42 (1975), 751-753. (1975) MR0402101DOI10.1215/S0012-7094-75-04262-3
  7. Grafakos, L., Classical and modern Fourier analysis, Prentice Hall (2004). (2004) Zbl1148.42001MR2449250
  8. Jevtic, M., Pavlovic, M., Shamoyan, R., A note on diagonal mapping theorem in spaces of analytic functions in the unit polydisk, Publ. Math. Debrecen 74/1-2 (2009), 1-14. (2009) MR2490421
  9. Mazya, V., Sobolev Spaces, Springer-Verlag, New York (1985). (1985) MR0817985
  10. Ren, G., Shi, J., 10.4064/sm163-2-1, Studia Math. 2 (2004), 103-117. (2004) Zbl1050.32006MR2047374DOI10.4064/sm163-2-1
  11. Rudin, W., Function theory in polydisks, Benjamin, New York (1969). (1969) MR0255841
  12. Shamoian, F. A., Embedding theorems and characterization of traces in the spaces H p ( U n ) , p ∈ ( 0 , ∞ ) , Mat. Sbornik, Russian 3 (1978), 709-725. (1978) 
  13. Shamoian, F. A., Diagonal mapping and questions of representations in spaces of holomorphic functions in polydisk, Siberian Math. J. Russian 31 (1990), 197-215. (1990) MR1065594
  14. Shamoyan, R. F., On the action of Hankel operators in bidisk and subspaces in H ∞ connected with inner functions in the unit disk, Doklady BAN, Bulgaria 60 (2007), 929-934. (2007) Zbl1145.47025MR2368752
  15. Seneta, E., Regularly varying functions, Springer-Verlag, New York (1976). (1976) Zbl0324.26002MR0453936
  16. Shapiro, J., 10.1215/S0012-7094-76-04316-7, Duke Math. J. 43 (1976), 187-202. (1976) MR0500100DOI10.1215/S0012-7094-76-04316-7
  17. Li, Songxiao, Shamoyan, R. F., On some properties of a differential operator on the polydisk, Banach J. Math. Anal. (2009), 68-84. (2009) MR2461748
  18. Verbitsky, I., Multipliers in spaces with fractional norms and inner functions, Siberian Math. J. Russian 150 (1985), 51-72. (1985) MR0788329

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.