دورية أكاديمية
Convexities of Gaussian integral means and weighted integral means for analytic functions
| العنوان: | Convexities of Gaussian integral means and weighted integral means for analytic functions |
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| المؤلفون: | Li, Haiying, Liu, Taotao |
| بيانات النشر: | Institute of Mathematics, Academy of Sciences of the Czech Republic Matematický ústav AV ČR |
| سنة النشر: | 2019 |
| المجموعة: | DML-CZ (Czech Digital Mathematics Library) |
| مصطلحات موضوعية: | keyword:Gaussian integral means, keyword:weighted integral means, keyword:analytic function, keyword:\nobreak convexity, msc:30H10, msc:30H20 |
| الوصف: | summary:We first show that the Gaussian integral means of $f\colon \mathbb {C}\to \mathbb {C}$ (with respect to the area measure ${\rm e}^{-\alpha |z|^{2}} {\rm d} A(z)$) is a convex function of $r$ on $(0,\infty )$ when $\alpha \leq 0$. We then prove that the weighted integral means $A_{\alpha ,\beta }(f,r)$ and $L_{\alpha ,\beta }(f,r)$ of the mixed area and the mixed length of $f(r\mathbb {D})$ and $\partial f(r\mathbb {D})$, respectively, also have the property of convexity in the case of $\alpha \leq 0$. Finally, we show with examples that the range $\alpha \leq 0$ is the best possible. |
| نوع الوثيقة: | text |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 0011-4642 1572-9141 |
| العلاقة: | mr:MR3959963; zbl:Zbl 07088803; reference:[1] Al-Abbadi, M. H., Darus, M.: Angular estimates for certain analytic univalent functions.Int. J. Open Problems Complex Analysis 2 (2010), 212-220.; reference:[2] Cho, H. R., Zhu, K.: Fock-Sobolev spaces and their Carleson measures.J. Funct. Anal. 263 (2012), 2483-2506. Zbl 1264.46017, MR 2964691, 10.1016/j.jfa.2012.08.003; reference:[3] Duren, P. L.: Univalent Functions.Grundlehren der Mathematischen Wissenschaften 259, Springer, New York (1983). Zbl 0514.30001, MR 0708494; reference:[4] Nehari, Z.: The Schwarzian derivative and schlicht functions.Bull. Am. Math. Soc. 55 (1949), 545-551. Zbl 0035.05104, MR 0029999, 10.1090/S0002-9904-1949-09241-8; reference:[5] Nunokawa, M.: On some angular estimates of analytic functions.Math. Jap. 41 (1995), 447-452. Zbl 0822.30014, MR 1326978; reference:[6] Peng, W., Wang, C., Zhu, K.: Convexity of area integral means for analytic functions.Complex Var. Elliptic Equ. 62 (2017), 307-317. Zbl 1376.30041, MR 3598979, 10.1080/17476933.2016.1218857; reference:[7] Wang, C., Xiao, J.: Gaussian integral means of entire functions.Complex Anal. Oper. Theory 8 (2014), 1487-1505 addendum ibid. 10 495-503 2016. Zbl 1303.30024, MR 3261708, 10.1007/s11785-013-0339-x; reference:[8] Wang, C., Xiao, J., Zhu, K.: Logarithmic convexity of area integral means for analytic functions II.J. Aust. Math. Soc. 98 (2015), 117-128. Zbl 1316.30050, MR 3294311, 10.1017/S1446788714000457; reference:[9] Wang, C., Zhu, K.: Logarithmic convexity of area integral means for analytic functions.Math. Scand. 114 (2014), 149-160. Zbl 1294.30104, MR 3178110, 10.7146/math.scand.a-16643; reference:[10] Xiao, J., Xu, W.: Weighted integral means of mixed areas and lengths under holomorphic mappings.Anal. Theory Appl. 30 (2014), 1-19. Zbl 1313.32024, MR 3197626, 10.4208/ata.2014.v30.n1.1; reference:[11] Xiao, J., Zhu, K.: Volume integral means of holomorphic functions.Proc. Am. Math. Soc. 139 (2011), 1455-1465. Zbl 1215.32002, MR 2748439, 10.1090/S0002-9939-2010-10797-9; reference:[12] Zhu, K.: Analysis on Fock Spaces.Graduate Texts in Mathematics 263, Springer, New York (2012). Zbl 1262.30003, MR 2934601, 10.1007/978-1-4419-8801-0 |
| الإتاحة: | https://doi.org/10.21136/CMJ.2018.0432-17Test http://hdl.handle.net/10338.dmlcz/147743Test |
| حقوق: | access:Unrestricted ; rights:DML-CZ Czech Digital Mathematics Library, http://dml.czTest/ ; rights:Institute of Mathematics AS CR, http://www.math.cas.czTest/ ; conditionOfUse:http://dml.cz/useTest |
| رقم الانضمام: | edsbas.B26E5052 |
| قاعدة البيانات: | BASE |
Full Text Finder | تدمد: | 00114642 15729141 |
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