You do realise that in the current worldwide environment we are in a period of deflation not inflation.
Therefore I would say in an environment of real estate prices remaining the same in nominal terms (If it does indeed occur) you will see low or no inflation.
In Fact Nice One, in a deflationary environment Fixed Assets such as real estate gain in real terms in the prices of everyday goods and services are falling around it. (Again presuming prices for real estate stagnate whilst goods/services deflate).
This can easily occur as everyday consumable goods/services have much higher demand/supply elasticity than fixed assets which are slower to react.
So to say that if real estate maintains a current price floor, but causes investment losses due to inflation is discounting the effect a slowing/recession economy will have on inflation itself.