HARDY-AMALGAM SPACES WITH VARIABLE EXPONENTS AND THEIR DUALS
Keywords:
amalgam spaces, dual spaces, Hardy-amalgam spaces, variable exponents spaces.DOI:
https://doi.org/10.17654/2277141722006Abstract
We introduce some new spaces termed as Hardy-amalgam spaces with variable exponents denoted $\mathcal{H}^{p(\cdot), q}(q>1)$. These spaces are defined via the maximal function characterization on the Euclidean space $\mathbb{R}^d$, by replacing Lebesgue quasi-norms by Wiener amalgam ones. We then investigate their dual spaces.
Received: January 18, 2022
Revised: April 11, 2022
Accepted: April 23, 2022
References
Able Zobo Vincent De Paul, Espaces de Hardy-amalgames et Etudes de quelques opérateurs classiques, Universite Felix Houphouet-Boigny, 2019.
I. Aydin, On variable exponent amalgam spaces, Analele Stiintifice ale Universitatii Ovidius Constanta 20(3) (2012), 5-20.
I. Aydin and A. T. Gurkanli, Weighted variable exponent amalgam spaces $Wleft(L^{p(x)} ; L_w^qright)$, Glas. Mat. 47(67) (2012), 165-174.
D. Cruz-Uribe, A. Fiorenza, J. M. Martell and C. Pérez, The boundedness of classical operators on variable spaces, Ann. Acad. Sci. Fenn. Math. 31(1) (2006), 239-264.
E. Nakai and Y. Sawano, Hardy spaces with variable exponents and generalized Campanato spaces, J. Funct. Anal. 262 (2012), 3665-3748.
E. Nakai and Y. Sawano, Orlicz-Hardy spaces and their dual, Sci. China Math. 57 (2014), 903-962. Doi: 10.1007/S11425-014-4798-y.
Ismail Aydin and Cihan Unal, Amalgam spaces with variable exponent, Conference Proceedings of Science and Technology 2(1) (2019), 22-26.
J. Feuto, Amalgames de Wiener, espaces de Morrey et application, EMA-Yaoundé, 2015.
J. García-Cuerva and J. L. Rubio de Francia, Weighted norm inequalities and related topics, Volume 116 of North-Holland Mathematics Studies, North-Holland Publishing Co., Amsterdam, 1985.
V. Kokilashvili, A. Meskhi and A. Zaighum, Weighted kernel operators in variable exponent amalgam spaces, J. Inequal. Appl. 1 (2013), Article number 173, 173-199. https://doi.org/10.1186/1029-242X-2013-173.
O. Kulak and A. T. Gurkanli, Bilinear multipliers of weighted Wiener amalgam spaces and variable exponent Wiener amalgam spaces, J. Inequal. Appl. 2014, 2014:476, 23 pp.
L. Diening, Maximal function on generalized Lebesgue spaces $L^{p(cdot)}$, Math. Inequal. Appl. 7(2) (2004), 245-253.
L. Diening, Maximal function on Musielak-Orlicz spaces and generalized Lebesgue spaces, Bull. Sci. Math. 129(8) (2005), 657-700.
L. Diening and M. Ruzicka, Calderón-Zygmund operators on generalized Lebesgue spaces $L^{p(cdot)}$ and problems related to fluid dynamics, J. Reine Angew. Math. 563 (2003), 197-220.
L. Diening, P. Harjulehto, P. Hästö, Y. Mizuta and T. Shimomura, Maximal functions in variable exponent spaces: limiting cases of the exponent, Ann. Acad. Sci. Fenn. Math. 34(2) (2009), 503-522.
O. Kovácik and J. Rákosník, On spaces $L^{p(x)}$ and $W^{k, p(x)}$, Czechoslovak Math. J. 41(4) (1991), 592-618.
René Erlín Castillo, Julio C. Ramos Fernández and Eduard Trousselot, Hardy-type spaces and its dual, Proyecciones 33(1) (2014), 43-59.
TRAORE Lassane, Molecular characterization of Hardy amalgam spaces with variable exponents and its application, Far East J. Math. Sci. (FJMS) 130(2) (2021), 117-134.
Takahiro Noi, Duality of variable exponent Triebel-Lizorkin and Besov spaces, J. Funct. Spaces Appl. 2012, Art. ID 361807, 19 pp.
https://doi.org/10.1155/2012/361807.
V. Kokilashvili, N. Samko and S. Samko, The maximal operator in weighted variable spaces $L^{p(cdot)}$, J. Funct. Spaces Appl. 5(3) (2007), 299-317.
Z. V. P. Ablé and J. Feuto, Dual of Hardy amalgam spaces and norms inequalities, Anal. Math. 45(4) (2019), 647-686.
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