• Target reported earnings that beat Wall Street's estimates.
• Presidents Biden and Xi prepare to meet in San Francisco.
• Mortgage demand picked up as interest rates declined.

Here are the most important news items that investors need to start their trading day:

1. Cool inflation, hot market

Boom. Softer-than-expected inflation data juiced stock markets Tuesday, giving the S&P 500 its best day since April. The Nasdaq jumped more than 2%, while the Dow, boosted in part by a strong post-earnings performance by Home Depot, surged nearly 500 points. Markets are on fire this month, as signs of moderation in the economy have put the chill on Treasury yields and spurred hope that the Federal Reserve is done with rate hikes. The producer price index, another inflation reading, is due Wednesday morning. Looking ahead, we might dodge a government shutdown this week, as the House passed a funding bill with bipartisan support, sending it to the Senate. Follow live market updates.

2. Mortgage pulse

Declining rates last week fueled mortgage demand, which hit its highest point in five weeks, according to the Mortgage Bankers Association. This week, meanwhile, mortgage rates continued their slide following a decline in Treasury yields spurred by the soft inflation reading. Still, the rate on the popular 30-year fixed-rate mortgage remains somewhat high, above 7%, compared with the three-handles we saw during the earlier days of the Covid pandemic. That rate could head back down to the 6% range by springtime, according to Lawrence Yun, the National Association of Realtors' chief economist.

3. San Francisco meet

President Joe Biden and Chinese leader Xi Jinping are set to meet Wednesday in San Francisco as the U.S. and China try to tamp down escalating trade and military tensions. The Biden administration has tried to manage expectations about a potential breakthrough, however. Still, Wall Street is cautiously optimistic about the summit, Pia Singh writes for CNBC Pro, as investors will likely be happy with merely an agreement for more frequent talks between the two sides.

4. Target posts big profit beat

Target reported profit that easily topped Wall Street's expectations this morning. The discounter has come under pressure recently for flagging sales as it sought to rejigger its inventory after a glut of unwanted products weighed on profits. While the company has made progress on the inventory front, which weighed heavily on the bottom line a year earlier, sales are still tricky. Shoppers are sticking mostly to essential items when they hit stores, and not spending so much on the discretionary items for which Target is famous. Still, investors liked what they saw from the earnings report, sending Target shares up double digits in premarket trading.

5. Core business

Apple gets a whopping 36% of Safari search revenue from Google, Alphabet CEO Sundar Pichai confirmed in testimony Tuesday. The arrangement between the two tech giants, which gives Google default search engine status on Apple's devices, is at the center of the Justice Department's antitrust case regarding the deal. But the subject came up in legal proceedings for a different case: Fortnight maker Epic Games' lawsuit against Google. An expert witness testifying on Google's behalf unexpectedly revealed the Apple search payment percentage Monday.

– CNBC's Lisa Kailai Han, Chelsey Cox, Diana Olick, Pia Singh, Melissa Repko, Jennifer Elias and Rohan Goswami contributed to this report.

— Follow broader market action like a pro on CNBC Pro.