Private equity firm Blackstone Group's chief executive said the worst of the industry's slump is behind it, and dealflow and IPO investments are opening up again.

We've all been through a trying period, Stephen Schwarzman said on Wednesday in a speech at the Super Return Middle East private equity conference in Dubai.

The future looks brighter and he is seeing more than green shoots of recovery, though the scale of economic growth through next year is still unclear.

We do not expect the U.S. economy to slip back into recession, but we do believe that weak consumer spending and continued constraints on bank lending will dampen the U.S. economic recovery in 2010 and 2011, Schwarzman said.

He is evaluating the prospects for up to seven IPOs, in addition to one already filed, which he said were spread across a variety of sectors and geographies.

There are also signs of life in the bank financing market, he said. We can certainly do transactions in the $3 billion to $4 billion range at this stage in the cycle, he said on the sidelines of the conference.

And with low leverage involved, deals of that size can use in excess of $1 billion equity.

Schwarzman sees the opportunity for more deals ahead but noted Blackstone had been outbid by strategics -- meaning companies rather than private equity firms -- on several occasions.

He said Blackstone is open to investing in the Middle East and sees the firm opening an office somewhere in the region. He declined to specify which city.

Schwarzman earlier made some of the details of his speech available to investors in Blackstone's funds.

(editing by John Stonestreet)