Despite slowing home sales, brokers in the Hamptons say the summer rental market remains strong, as foreigners are drawn by the weak dollar and the region’s beaches. The president of Town & Country Real Estate, Judi Desiderio, said her firm has rented about 19 percent of its properties this year to foreigners, compared to just 5 percent last year. The Southampton branch of Engel & Völkers, a brokerage based in Germany, reports that its rental business with foreigners has increased by about 10 percent this year. Prudential Douglas Elliman CEO Dottie Herman said rentals are “better than last year,” partly because many potential buyers have chosen instead to rent. As The Real Deal reported yesterday, home sales on Long Island’s East End fell 41 percent in the first quarter compared to last year and 35 percent compared to the last quarter, according to a report published by the appraisal firm Miller Samuel and Prudential Douglas Elliman.