Abstract
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.
Original language | English |
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Pages (from-to) | 291-302 |
Number of pages | 12 |
Journal | Georgian Mathematical Journal |
Volume | 25 |
Issue number | 2 |
DOIs | |
Publication status | Published - Jun 1 2018 |
Externally published | Yes |
Keywords
- Grand Lebesgue sequence space
- Hardy operator
- Hilbert transform
- convolution operator
- fractional operator
- maximal operator
ASJC Scopus subject areas
- General Mathematics