I also had trouble with my 110v sustaining the compressor- couldn't even start. So I wired a female plug directly onto the breaker panel. Hot went to the 15amp breakers 'breaked' side, nuetral to the neutral bus bar, and ground to, well ground (conduit). Now it works like a charm (and supposably the motor may pull like 25amps on start up- but it works on my 15amp 5 footer circuit!). And I didn't have access to a power panel cutoff either before I did it- (just be vawry vawry careful and don't touch live side of breaker!!!!! shut breaker off and wire to disconnected 'breaked' side only!!!! Use $12 inductive voltage tester- looks like a red pen- to 'see' and verify that the power is exactly where you think it is and that it is not flowing where you think it is not).
EDITED notes; The $12 inductive voltage tester is like a magic wand. Inductive because it doesn't have to touch anything. It 'sees' voltage through insulation by detecting the electromagnetic pulses of A/C. Use it to check every single wire and see were the current is. Never touch or work on anything that is live. Also- I had to shut off ALL the breakers on my panel inorder to cut off any current flowing back onto the neutral bus bar before I could touch anything. It's not very nuetral if there is current there! If you can pull the general cutoff to the whole panel- ofcourse do that- but my neighbors wouldn't like me then
(check again with your tester!). I just didn't go near the hot side of the breaker, broke every circuit after the breakers via tripping all breakers, verified no current present anywhere I needed to work, and wired my pig tails for a plug/shorty extension chord into the whole shabang.
I also killed my kitchen circuit by doing my MIG welding from it. Worked long enough to get the job done- now I just have to fix the kitchen to eat again.
Basically- you're aiming for one thing- to use the shortest distance of wire possible to get the power to your compressor and welder. The longer it is, the more resistance you get (same as wire gauge). Garbage disposals circuits may work ok as well since they are often a dedicated circuit back to the breaker. There's nothing wrong with your 110v coming in from the street. What's wrong is that you probably live in an old building with thin guage (higher resistance) wire running all over the place for long streches.
Disclaimer- if you don't feel like you know what your doing with 110v-
DON'T DO IT. There's no 'let's try this wire- I got a 50/50 chance' allowed. And always always verify and reverify that a ciruit is not live with the magic wand- even immediately before you intend to touch it, even though you already checked, check again.