Let $0 ＜p\leq1＜q＜\infty$, and $\omega_{1},\omega_{2}\in A_{1}$ (Muckenhoupt-class). We study an oscillating multiplier operator $T_{\gamma ,\beta }$ and obtain that it is bounded on the homogeneous weighted Herz-type Hardy spaces $H\dot{K}_{q}^{\alpha ,p}(\mathbb{R}^{n};\omega _{1},\omega _{2})$ when $\gamma=\frac{n\beta }{2}, \alpha =n(1-1/q)$. Also, for the unweighted case, we obtain the $H\dot{K}_{q}^{\alpha ,p}(\mathbb{R}^{n})$ boundedness of $T_{\gamma ,\beta }$ under certain conditions on $\gamma$. These results are substantial improvements and extensions of the main results in the papers by Li and Lu and by Cao and Sun. As an application, we prove the $H\dot{K}_{q}^{\alpha ,p}(\mathbb{R}^{n})$ boundedness of the spherical average $S_{t}^{\delta}$ uniformly on $t>0$.
Ziyao LIU
,
Dashan FAN
. CERTAIN OSCILLATING OPERATORS ON HERZ-TYPE HARDY SPACES[J]. Acta mathematica scientia, Series B, 2025
, 45(2)
: 310
-326
.
DOI: 10.1007/s10473-025-0202-y
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