A partial hot-water loss is still the landlord’s job
No hot water at only some faucets usually points to a plumbing problem in those lines or fixtures — still generally the landlord's responsibility to diagnose and repair as part of keeping the plumbing in working order.
When the whole unit loses hot water, the water heater is often the cause. When only one sink or shower lacks it, the problem may be in that fixture, a shutoff valve, or a specific line. Either way, maintaining the plumbing that delivers hot water throughout the unit is the landlord's duty.
Report which fixtures are affected and which still work, since that detail helps a plumber pinpoint the issue faster. A partial loss of hot water is still a real problem if it affects a fixture you need, like the shower. If your landlord ignores hot water missing from parts of your home, a free review can help you understand your options.
This is general information about California tenant rights, not legal advice. Every situation is different.