Many brands have responded with a rapid expansion of their store networks, turning what were once economic and fashion backwaters in China and Southeast Asia into high-end shopping havens.

LVMH Moët Hennessy Louis Vuitton, the biggest luxury group in the world, is a prime example. Last year, it generated about 6.9 billion euros ($9.7 billion) in revenue in Asia, where it operates more than 800 stores. That compares with 4.6 billion euros in revenue, and 570 stores, in the United States.

Ermenegildo Zegna, the Italian men’s wear company, which opened its first shop in Beijing in 1991, is also increasing its presence. It now has more than 70 stores in Greater China — mainland China, Hong Kong and Taiwan — making it Zegna’s biggest international market.

Prada has lagged some other companies in terms of expansion in mainland China. But about half of its 319 outlets around the world are in the Asia-Pacific region, more than a dozen of them in Hong Kong.

Prada, whose handbags and Miu Miu dresses can cost more than $1,000, plans to open dozens more stores, using some of the proceeds from the $2.1 billion it raised in its initial stock offering.

Market nervousness about the debt crisis in Greece and the prospect for global economic growth diminished Prada’s debut on Friday, the same way it did for the luggage maker Samsonite earlier this month.

Prada shares edged up 0.3 percent, closing at 39.6 Hong Kong dollars ($5.08) on the first day of trading. The modest rise contrasts with the large jumps in share prices of Internet companies like LinkedIn that recently have listed in New York.