TY - JOUR
T1 - Grand Lebesgue sequence spaces
AU - Rafeiro, Humberto
AU - Samko, Stefan
AU - Umarkhadzhiev, Salaudin
N1 - Funding Information:
Funding: The first author was partially supported by Pontificia Universidad Javeriana under the research project with ID PPT: 7272. The second and third authors were partially supported by Grant 18-01-00094-a of Russian Foundation of Basic Research.
Publisher Copyright:
© 2018 Walter de Gruyter GmbH, Berlin/Boston 2018.
PY - 2018/6/1
Y1 - 2018/6/1
N2 - We introduce grand Lebesgue sequence spaces and study various operators of harmonic analysis in these spaces, e.g., maximal, convolution, Hardy, Hilbert, and fractional operators, among others. Special attention is paid to fractional calculus, including the density of the discrete version of a Lizorkin sequence test space in vanishing grand spaces.
AB - We introduce grand Lebesgue sequence spaces and study various operators of harmonic analysis in these spaces, e.g., maximal, convolution, Hardy, Hilbert, and fractional operators, among others. Special attention is paid to fractional calculus, including the density of the discrete version of a Lizorkin sequence test space in vanishing grand spaces.
KW - Grand Lebesgue sequence space
KW - Hardy operator
KW - Hilbert transform
KW - convolution operator
KW - fractional operator
KW - maximal operator
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U2 - 10.1515/gmj-2018-0017
DO - 10.1515/gmj-2018-0017
M3 - Article
AN - SCOPUS:85047079493
SN - 1072-947X
VL - 25
SP - 291
EP - 302
JO - Georgian Mathematical Journal
JF - Georgian Mathematical Journal
IS - 2
ER -