<abstract><p>In this paper, we first show that the $ p $-adic version of maximal function $ \mathcal{M}_{L\log L}^{p} $ is equivalent to the maximal function $ \mathcal{M}^{p}(\mathcal{M}^{p}) $ and that the class of functions for which the maximal commutators and the commutator with the $ p $-adic version of maximal function or the maximal sharp function are bounded on the $ p $-adic vector spaces are characterized and proved to be the same. Moreover, new pointwise estimates for these operators are proved.</p></abstract>
In this paper, we obtain the sharp bound for fractional conjugate Hardy operator on higher-dimensional product spaces from L1ℝn1×⋯×ℝnm to the space wLQℝn1×⋯×ℝnm and Lpℝn1×⋯×ℝnm to the space Lqℝn1×⋯×ℝnm. More generally, the operator norm of the fractional Hardy operator on higher-dimensional product spaces from LPℝn1×⋯×ℝnm to LQIℝn1×⋯×ℝnm is obtained.
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