Average rents for apartments, offices and retail space are continuing their upswing, but the rate of increase is flat or slowing down.

The average apartment rent in the U.S. in the third quarter was $1,090, according to research firm Reis, Inc. That’s an increase of 0.8%, down from 1.1% in the previous quarter.

The apartment vacancy rate was 4.6%, down from 4.7% in the second quarter. That’s a big drop from the roughly 8% rate in late 2009.

The average rent for office space in the third quarter was $28.23 per square foot, an increase of 0.2%. The vacancy rate dropped from 17.2% to 17.1%.

The biggest jump in office rents was in San Francisco, which saw a 4.1% increase over three months. Increases of 2% or more were reported in New York, San Jose, Houston and Austin. The biggest drop (1%) was in Las Vegas.

Occupied office space increased by 5.4 million square feet in the third quarter. Overall, the amount of occupied space has expanded by 36.7 million square feet since the beginning of 2011. But that’s not nearly as large as the decrease of 141 million square feet that occurred between 2008 and 2010.

The average rent for mall space was $39.24 per square foot last quarter, an increase of 0.3%. The average shopping center rent was $16.57 per square foot, an increase of 0.1%.

Vacancy rates were 8.7% for malls and 10.8% for shopping centers.