Yes, absolutely, provided of course the 3/3 and the 4/4 don't have trample or anything else special about assigning combat damage. Thanks to Brave the Sands, your 1/1 can block both. Both will be blocked creatures, and blocked creatures can't assign combat damage to the defending player without having trample or some other ability. They will have to assign all their damage to the blocker, no matter how small it is.
To note, even if the 1/1 is removed somehow during the declare blockers step, after blocking but before combat damage, the attacking creatures still remain blocked until end of combat, and they still can't assign combat damage to the player or planeswalker they're attacking. If there is no blocker left come the combat damage step, they just don't deal combat damage at all.
I'm a former judge (lapsed), who keeps up to date on rules and policy. Keep in mind that judges' answers aren't necessarily more valid than those of people who aren't judges; what matters is we can quote the rules to back up our answers. When in doubt, ask for such quotes.
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To note, even if the 1/1 is removed somehow during the declare blockers step, after blocking but before combat damage, the attacking creatures still remain blocked until end of combat, and they still can't assign combat damage to the player or planeswalker they're attacking. If there is no blocker left come the combat damage step, they just don't deal combat damage at all.