Inflation will actually be high in the United States and the eurozone, probably until the summer of 2022, but this is not necessarily negative for equities, on the contrary. Economists at Natixis believe that in the current configuration, inflation will drive share prices up and not down. 

Inflation is not necessarily bad for equities

“If nominal wages react less than proportionately to inflation, a rise in producer prices will push down real wages and drive up earnings. If nominal interest rates rise less than inflation, inflation will push down real interest rates.”

“If inflation leads to higher earnings and lower real interest rates, it is conducive to a rise in stock market indices. So we should stop writing that inflation threatens equity markets.”