Usually, the condition that T is bounded on L^2(R^n) is assumed to prove the boundedness of an operator T on a Hardy space. With this assumption, one only needs to prove the uniformly boundness of T on atoms, since T(...Usually, the condition that T is bounded on L^2(R^n) is assumed to prove the boundedness of an operator T on a Hardy space. With this assumption, one only needs to prove the uniformly boundness of T on atoms, since T(f)=∑iλi T(ai), provided that f =∑iλiai in L^2(R^n), where ai is an L^2 atom of this Hardy space. So far, the L^2 atomic decomposition of local Hardy spaces h^p(R^n), 0 < p ≤ 1, hasn't been established. In this paper, we will solve this problem, and also show that h^p(R^n) can also be characterized by discrete Littlewood-Paley functions.展开更多
In this work, we presented a new law which was based on the well-known duality property for the set identities. We introduced the diagrams that could be applied to the proof for the set identities. Some prime examples...In this work, we presented a new law which was based on the well-known duality property for the set identities. We introduced the diagrams that could be applied to the proof for the set identities. Some prime examples were also provided to illustrate the proposed law.展开更多
基金Supported by NNSF of China(Grant Nos.11501308 and 11771223)
文摘Usually, the condition that T is bounded on L^2(R^n) is assumed to prove the boundedness of an operator T on a Hardy space. With this assumption, one only needs to prove the uniformly boundness of T on atoms, since T(f)=∑iλi T(ai), provided that f =∑iλiai in L^2(R^n), where ai is an L^2 atom of this Hardy space. So far, the L^2 atomic decomposition of local Hardy spaces h^p(R^n), 0 < p ≤ 1, hasn't been established. In this paper, we will solve this problem, and also show that h^p(R^n) can also be characterized by discrete Littlewood-Paley functions.
文摘In this work, we presented a new law which was based on the well-known duality property for the set identities. We introduced the diagrams that could be applied to the proof for the set identities. Some prime examples were also provided to illustrate the proposed law.
