OK! Now I get:
Code:
Starting WebServerAP on TEENSY 4.0 with ESP8266-AT & ESP8266_AT_WebServer Library
ESP8266_AT_WebServer v1.6.0
[ESP_AT] Use ES8266-AT Command
WiFi shield init done
Attempting to start AP with SSID = EFD_NET and PW = 12345678
Access point started @ channel 2
AP IP Address = 192.168.120.1
SSID: EFD_NET, PASS: 12345678
WebServer started @ 192.168.120.1
To see this page in action, open a browser to http://192.168.120.1
and

I am using the 3.3v supply from the T4. The PJRC data sheet says that it can supply up to 250mA, and the data sheet for the ESP-01 (but not sure its exactly the right one) says that the highest (typical) power requirement (in one mode) is 215mA. I'll only be using the WiFi interface intermittently, so hopefully I can get away with it. I'll check to see if there's a way to constrain it to the lower-power modes, since speed isn't that important for my application. I use T4s to control LED lighting for large art installations, and I want a WiFi interface to occasionally adjust settings/modes.
Thanks SO MUCH for your help. BTW, you appear to be amazingly productive. Wow.