Generalized Hölder type spaces of harmonic functions in the unit ball and half space

Alexey Karapetyants; Joel Esteban Restrepo

Czechoslovak Mathematical Journal (2020)

  • Volume: 70, Issue: 3, page 675-691
  • ISSN: 0011-4642

Abstract

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We study spaces of Hölder type functions harmonic in the unit ball and half space with some smoothness conditions up to the boundary. The first type is the Hölder type space of harmonic functions with prescribed modulus of continuity ω = ω ( h ) and the second is the variable exponent harmonic Hölder space with the continuity modulus | h | λ ( · ) . We give a characterization of functions in these spaces in terms of the behavior of their derivatives near the boundary.

How to cite

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Karapetyants, Alexey, and Restrepo, Joel Esteban. "Generalized Hölder type spaces of harmonic functions in the unit ball and half space." Czechoslovak Mathematical Journal 70.3 (2020): 675-691. <http://eudml.org/doc/297377>.

@article{Karapetyants2020,
abstract = {We study spaces of Hölder type functions harmonic in the unit ball and half space with some smoothness conditions up to the boundary. The first type is the Hölder type space of harmonic functions with prescribed modulus of continuity $\omega =\omega (h)$ and the second is the variable exponent harmonic Hölder space with the continuity modulus $|h|^\{\lambda (\cdot )\}$. We give a characterization of functions in these spaces in terms of the behavior of their derivatives near the boundary.},
author = {Karapetyants, Alexey, Restrepo, Joel Esteban},
journal = {Czechoslovak Mathematical Journal},
keywords = {Hölder space; harmonic function; variable exponent space; modulus of continuity},
language = {eng},
number = {3},
pages = {675-691},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Generalized Hölder type spaces of harmonic functions in the unit ball and half space},
url = {http://eudml.org/doc/297377},
volume = {70},
year = {2020},
}

TY - JOUR
AU - Karapetyants, Alexey
AU - Restrepo, Joel Esteban
TI - Generalized Hölder type spaces of harmonic functions in the unit ball and half space
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 3
SP - 675
EP - 691
AB - We study spaces of Hölder type functions harmonic in the unit ball and half space with some smoothness conditions up to the boundary. The first type is the Hölder type space of harmonic functions with prescribed modulus of continuity $\omega =\omega (h)$ and the second is the variable exponent harmonic Hölder space with the continuity modulus $|h|^{\lambda (\cdot )}$. We give a characterization of functions in these spaces in terms of the behavior of their derivatives near the boundary.
LA - eng
KW - Hölder space; harmonic function; variable exponent space; modulus of continuity
UR - http://eudml.org/doc/297377
ER -

References

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  1. Arsenović, M., Kojić, V., Mateljević, M., On Lipschitz continuity of harmonic quasiregular maps on the unit ball in ℝ n , Ann. Acad. Sci. Fenn., Math. 33 (2008), 315-318. (2008) Zbl1140.31003MR2386855
  2. Axler, S., Bourdon, P., Ramey, W., 10.1007/b97238, Graduate Texts in Mathematics 137, Springer, New York (2001). (2001) Zbl0959.31001MR1805196DOI10.1007/b97238
  3. Blumenson, L. E., 10.2307/2308932, Am. Math. Mon. 67 (1960), 63-66. (1960) MR1530579DOI10.2307/2308932
  4. 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
  5. 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
  6. Cruz-Uribe, D., Fiorenza, A., 10.1007/978-3-0348-0548-3, Applied and Numerical Harmonic Analysis, Birkhäuser/Springer, Heidelberg (2013). (2013) Zbl1268.46002MR3026953DOI10.1007/978-3-0348-0548-3
  7. 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
  8. Duren, P., Schuster, A., 10.1090/surv/100, Mathematical Surveys and Monographs 100, American Mathematical Society, Providence (2004). (2004) Zbl1059.30001MR2033762DOI10.1090/surv/100
  9. Hedenmalm, H., Korenblum, B., Zhu, K., 10.1007/978-1-4612-0497-8, Graduate Texts in Mathematics 199, Springer, New York (2000). (2000) Zbl0955.32003MR1758653DOI10.1007/978-1-4612-0497-8
  10. Karapetyants, A., Rafeiro, H., Samko, S., 10.1007/s11785-018-0780-y, Complex Anal. Oper. Theory 13 (2019), 275-289. (2019) Zbl1421.30070MR3905593DOI10.1007/s11785-018-0780-y
  11. Karapetyants, A., Samko, S., 10.1515/gmj.2010.028, Georgian Math. J. 17 (2010), 529-542. (2010) Zbl1201.30072MR2719633DOI10.1515/gmj.2010.028
  12. Karapetyants, A., Samko, S., 10.1134/S000143461607004X, Math. Notes 100 (2016), 38-48. (2016) Zbl1364.30063MR3588827DOI10.1134/S000143461607004X
  13. Karapetyants, A., Samko, S., 10.1080/17476933.2016.1140750, Complex Var. Elliptic Equ. 61 (2016), 1090-1106. (2016) Zbl1351.30042MR3500518DOI10.1080/17476933.2016.1140750
  14. Karapetyants, A., Samko, S., 10.1515/fca-2017-0059, Fract. Calc. Appl. Anal. 20 (2017), 1106-1130. (2017) Zbl1386.30052MR3721891DOI10.1515/fca-2017-0059
  15. Karapetyants, A., Samko, S., 10.1007/s10958-017-3538-6, J. Math. Sci., New York 226 (2017), 344-354. (2017) Zbl1386.30051MR3705149DOI10.1007/s10958-017-3538-6
  16. Karapetyants, A., Samko, S., 10.1007/s00009-018-1272-z, Mediterr. J. Math. 15 (2018), Paper No. 226, 17 pages. (2018) Zbl1411.30039MR3878666DOI10.1007/s00009-018-1272-z
  17. Karapetyants, A., Samko, S., 10.1515/gmj-2018-0027, Georgian Math. J. 25 (2018), 271-282. (2018) Zbl1392.30023MR3808288DOI10.1515/gmj-2018-0027
  18. Kokilashvili, V., Meskhi, A., Rafeiro, H., Samko, S., 10.1007/978-3-319-21015-5, Operator Theory: Advances and Applications 248, Birkhäuser/Springer, Basel (2016). (2016) Zbl1385.47001MR3559400DOI10.1007/978-3-319-21015-5
  19. Kokilashvili, V., Meskhi, A., Rafeiro, H., Samko, S., 10.1007/978-3-319-21018-6, Operator Theory: Advances and Applications 249, Birkhäuser/Springer, Basel (2016). (2016) Zbl1367.47004MR3559401DOI10.1007/978-3-319-21018-6
  20. Zhu, K., 10.1007/0-387-27539-8, Graduate texts in Mathematics 226, Springer, New York (2005). (2005) Zbl1067.32005MR2115155DOI10.1007/0-387-27539-8
  21. Zhu, K., 10.1090/surv/138, Mathematical Surveys and Monographs 138, American Mathematical Society, Providence (2007). (2007) Zbl1123.47001MR2311536DOI10.1090/surv/138

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