For low back, think about strengthening all aspects of the core, but also think about improving your hip mobility, and possibly hip flexor strength.
Often the low back gets tired because the hip flexors are no longer pulling their weight, causing reduced hip flexion. And when hip flexion is reduced but our movement still requires hip flexion (as in skiing), then our low back has to take over.
Two exercise suggestions for that:
- try a hip flexor strengthening exercise where you sit on the edge of a chair, maintaining a neutral spine (slight arch) and use your hands to lift one knee up toward your chest (don't lose that back arch). Then take your hands off your leg but don't let it fall (use the leg/hip muscles). Hold for 5 seconds and then slowly release. Do 5 reps on each side. If it is easy - double check that you are not flexing through the back.
Also think about stretching the hip flexor - try a half-kneeling lunge stretch for 2 reps of a 45 second hold daily.
For the core, don't do things like crunches as the flexion can be trouble for an already troubled back. Instead think of planks - but only hold as long as you can keep your form. As soon as your hips rise or your back sags, you're done. Pushing through at that point is doing nothing for your core strength, but may be contributing to back pain. Work on being able to hold for longer, while maintaining perfect form, each time you try.
Side planks and glute bridges are equally important - maybe even more important.
PS - for more, I have a couple articles on my website about low back pain:http://elsbethvaino.com/2009/11/lessons-about-low-back-pain-part-one/