Abstract
In the present article we obtain the boundedness for commutators of rough p -adic Hardy operator on p -adic central Morrey spaces. Furthermore, we also acquire the boundedness of rough p -adic Hardy operator on Lebesgue spaces.
Highlights
The classical Hardy operator for a non-negative function f : R+ ⟶ R+is given as 1 x ðx f ðtÞdt, x
The classical Hardy operator for a non-negative function f : R+ ⟶ R+is given as Hf ðxÞ =1 x ðx f ðtÞdt, x > 0: ð1ÞIn [1], Hardy defined the above operator which satisfies kH f kLrðR+Þ ≤ r r − k f kLr ðR+ Þ
We mainly focused on the boundedness for commutators of rough p-adic Hardy operator on p-adic central Morrey spaces
Summary
The classical Hardy operator for a non-negative function f : R+ ⟶ R+is given as 1 x ðx f ðtÞdt, x In [1], Hardy defined the above operator which satisfies kH f kLrðR+Þ Suppose p is a prime number, r ∈ Q, we introduce the p -adic norm jrjp by a rule j0jp = 0, jrjp = p−α, ð4Þ We denote the completion of Q in the norm j·jp by Qp: Any nonzero p-adic number can be written in series form as (see [14]):
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