The boundedness of certain sublinear operator in the weighted variable Lebesgue spaces
Czechoslovak Mathematical Journal (2010)
- Volume: 60, Issue: 2, page 327-337
- ISSN: 0011-4642
Access Full Article
topAbstract
topHow to cite
topBandaliev, Rovshan A.. "The boundedness of certain sublinear operator in the weighted variable Lebesgue spaces." Czechoslovak Mathematical Journal 60.2 (2010): 327-337. <http://eudml.org/doc/38010>.
@article{Bandaliev2010,
abstract = {The main purpose of this paper is to prove the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent. As an application we prove the boundedness of certain sublinear operators on the weighted variable Lebesgue space.},
author = {Bandaliev, Rovshan A.},
journal = {Czechoslovak Mathematical Journal},
keywords = {variable Lebesgue space; weights; Hardy operator; boundedness; variable Lebesgue space; weight; Hardy operator; boundedness},
language = {eng},
number = {2},
pages = {327-337},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The boundedness of certain sublinear operator in the weighted variable Lebesgue spaces},
url = {http://eudml.org/doc/38010},
volume = {60},
year = {2010},
}
TY - JOUR
AU - Bandaliev, Rovshan A.
TI - The boundedness of certain sublinear operator in the weighted variable Lebesgue spaces
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 2
SP - 327
EP - 337
AB - The main purpose of this paper is to prove the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent. As an application we prove the boundedness of certain sublinear operators on the weighted variable Lebesgue space.
LA - eng
KW - variable Lebesgue space; weights; Hardy operator; boundedness; variable Lebesgue space; weight; Hardy operator; boundedness
UR - http://eudml.org/doc/38010
ER -
References
top- Abbasova, M. M., Bandaliev, R. A., On the boundedness of Hardy operator in the weighted variable exponent spaces, Proc. of Nat. Acad. of Sci. of Azerbaijan. Embedding theorems. Harmonic Analysis. 13 (2007), 5-17. (2007) MR2719561
- Acerbi, E., Mingione, G., 10.1215/S0012-7094-07-13623-8, Duke Math. J. 136 (2007), 285-320. (2007) Zbl1113.35105MR2286632DOI10.1215/S0012-7094-07-13623-8
- Bandaliev, R. A., On an inequality in Lebesgue space with mixed norm and with variable summability exponent, Mat. Zametki 84 (2008), 323-333 Russian. (2008) Zbl1171.46023MR2473750
- Bradley, J., 10.4153/CMB-1978-071-7, Canadian Mathematical Bull. 21 (1978), 405-408. (1978) Zbl0402.26006MR0523580DOI10.4153/CMB-1978-071-7
- Cruz-Uribe, D., Fiorenza, A., Neugebauer, C. J., The maximal function on variable spaces, Ann. Acad. Sci. Fenn. Math. 28 (2003), 223-238. (2003) MR1976842
- Diening, L., Maximal function on generalized Lebesgue spaces , Math. Inequal. Appl. 7 (2004), 245-253. (2004) MR2057643
- Diening, L., Samko, S., Hardy inequality in variable exponent Lebesgue spaces, Frac. Calc. and Appl. Anal. 10 (2007), 1-18. (2007) Zbl1132.26341MR2348863
- Edmunds, D. E., Kokilashvili, V., 10.4153/CMB-1995-043-5, Canadian Math. Bull. 38 (1995), 295-303. (1995) Zbl0839.47022MR1347301DOI10.4153/CMB-1995-043-5
- Edmunds, D. E., Kokilashvili, V., Meskhi, A., On the boundedness and compactness of weighted Hardy operators in spaces , Georgian Math. J. 12 (2005), 27-44. (2005) MR2136721
- Edmunds, D. E., Kokilashvili, V., Meskhi, A., Bounded and compact integral operators, Math. and Its Applications. 543, Kluwer Acad.Publish., Dordrecht (2002). (2002) Zbl1023.42001MR1920969
- Edmunds, D. E., Kokilashvili, V., Meskhi, A., Two-weight estimates in spaces for classical integral operators and applications to the norm summability of Fourier trigonometric series, Proc. A. Razmadze Math. Inst. 142 (2006), 123-128. (2006) MR2294574
- Gadjiev, A. D., Aliev, I. A., Weighted estimates for multidimensional singular integrals generated by a generalized shift operator, Mat. Sbornik 183 (1992), 45-66 Russian. (1992) MR1198834
- Guliev, V. S., Two-weight inequalities for integral operators in -spaces and their applications, Trudy Mat. Inst. Steklov. 204 (1993), 97-116. (1993) MR1320021
- Guliev, V. S., Integral operators on function spaces defined on homogeneous groups and domains in Doctor’s dissertation, Mat. Inst. Steklov. (1994), 1-329. (1994)
- Harjulehto, P., Hästö, P., Koskenoja, M., Hardy's inequality in a variable exponent Sobolev space, Georgian Math. J. 12 (2005), 431-442. (2005) Zbl1096.46017MR2174945
- Kokilashvili, V., Meskhi, A., Two-weight inequalities for singular integrals defined on homogeneous groups, Proc. A. Razmadze Math. Inst. 112 (1997), 57-90. (1997) Zbl0983.43501MR1468962
- Kokilashvili, V., Samko, S. G., 10.1515/GMJ.2003.145, Georgian Math. J. 10 (2003), 145-156. (2003) MR1990694DOI10.1515/GMJ.2003.145
- Kokilashvili, V., Samko, S. G., The maximal operator in weighted variable spaces on metric measure space, Proc. A. Razmadze Math. Inst. 144 (2007), 137-144. (2007) MR2387413
- Kopaliani, T. S., 10.1007/s10587-004-6427-3, Czech. Math. J. 54 (2004), 791-805. (2004) Zbl1080.47040MR2086735DOI10.1007/s10587-004-6427-3
- Kováčik, O., Rákosník, J., On spaces and , Czech. Math. J. 41 (1991), 592-618. (1991) MR1134951
- Krbec, M., Opic, B., Pick, L., Rákosník, J., Some recent results on Hardy type operators in weighted function spaces and related topics, Function spaces, differential operators and nonlinear analysis (Frie4ichroda, 1992). 158-184, Teubner-Texte Math., 133, Teubner, Stuttgart (1993). (1993) MR1242582
- Lu, G., Lu, Sh., Yang, D., 10.1023/A:1016568918973, Analysis Math. 28 (2002), 103-134. (2002) Zbl1026.43007MR1918254DOI10.1023/A:1016568918973
- Mashiyev, R. A., Çekiç, B., Mamedov, F. I., Ogras, S., 10.1016/j.jmaa.2006.12.043, J. Math. Anal. Appl. 334 (2007), 289-298. (2007) MR2332556DOI10.1016/j.jmaa.2006.12.043
- Maz'ya, V. G., Sobolev Spaces, Springer-Verlag, Berlin-Heidelberg-New York (1985). (1985) Zbl0727.46017MR0817985
- Muckenhoupt, B., 10.4064/sm-44-1-31-38, Studia Math. 44 (1972), 31-38. (1972) Zbl0236.26015MR0311856DOI10.4064/sm-44-1-31-38
- Musielak, J., Orlicz Spaces and Modular Spaces, Lecture Notes in Math. 1034. Springer-Verlag, Berlin-Heidelberg-New York (1983). (1983) Zbl0557.46020MR0724434
- Musielak, J., Orlicz, W., 10.4064/sm-18-1-49-65, Studia Math. 18 (1959), 49-65. (1959) Zbl0099.09202MR0101487DOI10.4064/sm-18-1-49-65
- Nakano, H., Modulared semi-ordered linear spaces, Maruzen. Co., Ltd., Tokyo (1950). (1950) Zbl0041.23401MR0038565
- Nekvinda, A., Hardy-Littlewood maximal operator in , Math. Ineq. Appl. 7 (2004), 255-265. (2004) MR2057644
- Opic, B., Kufner, A., Hardy-Type Inequalities, Pitman Research Notes in Math. ser., 219. Longman sci. and tech., Harlow (1990). (1990) Zbl0698.26007MR1069756
- Orlicz, W., 10.4064/sm-3-1-200-211, Studia Math. 3 (1931), 200-212. (1931) Zbl0003.25203DOI10.4064/sm-3-1-200-211
- Růžička, M., Electrorheological Fluids: Modeling and Mathematical theory, Lecture Notes in Math. 1748. Springer-Verlag, Berlin (2000). (2000) MR1810360
- Samko, S. G., Differentiation and integration of variable order and the spaces , Proc.Inter.Conf. "Operator theory for Complex and Hypercomplex analysis". 1994, 203-219. Contemp. Math., 212, AMS, Providence, RI, 1998. MR1486602
- Samko, S. G., 10.1080/10652469808819191, Integ. Trans. and Special Funct. 7 (1998), 123-144. (1998) MR1658190DOI10.1080/10652469808819191
- Sharapudinov, I. I., On a topology of the space , Mat. Zametki 26 (1979), 613-637 Russian. (1979) MR0552723
- Sharapudinov, I. I., The basis property of the Haar system in the space and the principle of localization in the mean, Mat. Sbornik 130 (1986), 275-283 Russian. (1986) MR0854976
- Soria, F., Weiss, G., 10.1512/iumj.1994.43.43009, Indiana Univ. Math. J. 43 (1994), 187-204. (1994) Zbl0803.42004MR1275458DOI10.1512/iumj.1994.43.43009
- Zeren, Y., Guliyev, V. S., Two-weight norm inequalities for some anisotropic sublinear operators, Turkish Math. J. 30 (2006), 329-350. (2006) Zbl1179.42015MR2248753
- Zhikov, V. V., Averaging of functionals of the calculus of variations and elasticity theory, Izv. Akad. Nauk Russian 50 (1986), 675-710 Russian. (1986) Zbl0599.49031MR0864171
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.