An interesting point to add here. Most of us have operated under the assumption that the airports nearby (not Class B, C, D or surface E) only have to be notified and that they cannot deny permission. However, I was reading the FAA guidance documents that accompany Part 107 and in there the FAA says that if a regional or private airport said you shouldn't fly when you contact them that they (FAA) would consider it a violation if you were to fly. They argue that the law prevents interfering with air traffic and if you fly when any of these people say no, then you are interfering with air traffic.
I'm sure many would object to this interpretation of the law but until it is litigated somewhere, this is apparently the tact that FAA will take.
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You don't ask for permission. You notify and must monitor communication on CTAF like any other pilot.