The explosively growing demands for mobile traffic service bring both challenges and opportunities to wireless net- works, among which, wireless network virtualization is proposed as the main evolution towards 5G. In this paper, we first propose a Software Defined Network (SDN) based wireless virtualization architecture for enabling multi-flow transmission in order to save capital expenses (CapEx) and operation expenses (OpEx) significantly with multiple Infrastructures Providers (InPs) and multiple Mobile Virtual Network Operators (MVNOs). We for- mulate the virtual resource allocation problem with diverse QoS requirements as a social welfare maximization problem with transaction cost. Due to the high computational complexity of formulated problem and hidden information of InPs and MVNOs for SDN controller, we introduce the shadow price for ensuring the desirable economic properties as well as the total welfare of system. Simulations are conducted with different system configurations to show the effectiveness of the proposed SDN based wireless virtualization framework and double auction mechanism.