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The infinite pseudo-differential operator on  W   M  ( R   n  )   space is introduced and its various properties are studied. A general class of symbols  θ ( x , ξ )   is introduced and then it is proved that the pseudo-differential operator  A   θ   φ  is a continuous linear mapping from  W   M  ( R   n  )   into itself. An  L   p  ( R   n  )  -boundedness result for the pseudo-differential operator associated with a general class of symbols  σ ( x , ξ )   for  ξ  =  u + it  is obtained. It is shown that the pseudo-differential operator is a bounded linear operator from  L   p  ( R   n  )   into  L   p  ( R   n  )   for   1 &lt; p &lt; ∞  . The Sobolev space of type  G   s,p  ( R   n  )   is introduced and its properties are studied.

Infinite pseudo-differential operators on W M ( R n ) space