My biggest concern here is actually with the one along what seems to be the planet's "Equator". That is a zone where usually we have enough evaporation and the air flows up, chilling fast and raining. The wind coming from the sea in the west would most likely carry enough water to make that desert unlikely.
But then again, it IS a fantasy map, so if you want a desert, then let the desert be
Just for future reference, this site gives two examples of reasons for deserts forming. while there are others, these two are the most frequent.
jfrazierjr seems to be referring to the rain shadow effect, but I believe that wouldn't be much of a problem in the landscape you're building. Except that I'm not sure where the winds would be flowing: In a basic fashion, you'd have wind from world rotation going west, but being a coastal line, difference in temperatures during different times of day would make wind come and go from the land to the sea and the other way around.