[Objective]The representation of the dual space of harmonic Fock space promotes the study of properties of special operators such as self-adjoint operators,Toeplitz operators and dual operators on function Spaces.In addition,dual space theory plays a very important role in fields such as remote sensing,economics,computer communication,and quantum mechanics among others.Based on the research of harmonic Fock space,herein we study the concrete representation of the dual space of harmonic Fock space.[Methods]In this paper,a linear subspace of all reproducing kernels in harmonic Fock space is constructed and proved to be dense in harmonic Fock space.Then,by virtue of properties of functional on this dense subspace,we study the representation of the dual space of harmonic Fock space via discussing the dual space of analytic Fock space.[Results]We obtain two results for dual spaces of harmonic Fock spaces:when 1＜p＜∞,(Fph,α)*=Fqh,β,where1/p+1/q=1.When p=1,(F1h,α)*=F∞h,β.These two results correspond to the representation of the dual space of the harmonic Fock space when 1＜p＜∞ and p=1,respectively.In particular,if α=β,we also develop the following corollary:when 1≤p＜∞,(Fph,α)*=Fqh,α.[Conclusion]At present,the representation of the dual space of the harmonic Fock space has been obtained by classical methods.These results will be used in subsequent studies of harmonic Fock spaces.
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