Global share markets mostly fell as renewed gains in oil prices intensified concerns about inflation and higher-for-longer interest rates. Brent futures rose 2.1% to $106.49 a barrel, taking gains for September to almost 18%, while US crude added 1.5% to $93.84. US President Donald Trump rejected an Iranian proposal to reopen the Strait of Hormuz over the weekend, though he said talks would continue this week. A shortage of refining capacity has pushed diesel prices to all-time highs well above crude, increasing the risk that inflation becomes embedded in pricing and wage decisions. The Reserve Bank of Australia is likely to tighten policy at its Tuesday meeting, while markets price a 66% chance of a second consecutive Federal Reserve hike in October and about 90 basis points of tightening through late next year. Strong US, Asian and European economic activity, partly supported by AI investment, has helped sustain equity valuations despite rising yields. US 30-year Treasury yields reached 5.5185%, near their highest since 2004, while the dollar climbed to a two-month peak. Investors face a week of US inflation, GDP, manufacturing and labor data, including Friday's payrolls report.