TY - JOUR
T1 - Generalized Fourier Multipliers via Mittag-Leffler Functions
AU - Hawawsheh, Laith
AU - Al-Salman, Ahmad
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.
PY - 2024/2/20
Y1 - 2024/2/20
N2 - A Fourier multiplier related to Mittag-Leffler function is introduced. We prove that our multiplier is radial on Rnand generalizes the Bessel function. Furthermore, we study the L2 boundedness of the related Mittag-Leffler maximal function, the Littlewood–Paley g-function, and the discrete singular integral operator. We prove that the three operators are bounded on L2(Rn). In addition, our formulation of the introduced Mittag-Leffler maximal function is a solution of a diffusion equation. Our results generalize previously known results.
AB - A Fourier multiplier related to Mittag-Leffler function is introduced. We prove that our multiplier is radial on Rnand generalizes the Bessel function. Furthermore, we study the L2 boundedness of the related Mittag-Leffler maximal function, the Littlewood–Paley g-function, and the discrete singular integral operator. We prove that the three operators are bounded on L2(Rn). In addition, our formulation of the introduced Mittag-Leffler maximal function is a solution of a diffusion equation. Our results generalize previously known results.
KW - 42B25
KW - discrete singular integral operator
KW - Fourier transform
KW - Littlewood–Paley g-function
KW - Mittag-Leffler function
KW - Primary 42B20
KW - Secondary 42B15
KW - spherical maximal function
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UR - https://www.mendeley.com/catalogue/428ab3b3-22d0-327d-ac84-7f76d7f1e693/
U2 - 10.1007/s00009-024-02587-3
DO - 10.1007/s00009-024-02587-3
M3 - Article
AN - SCOPUS:85185477052
SN - 1660-5446
VL - 21
JO - Mediterranean Journal of Mathematics
JF - Mediterranean Journal of Mathematics
IS - 2
M1 - 49
ER -