"may hopefully" is a correct and usable part of a sentence in written English.
You can use it when indicating that something is likely or expected to happen. Example: If I study hard, I may hopefully pass the exam.
These results may hopefully advance the design of new bioactive glasses.
But our profession's indifference may hopefully soon be a thing of the past.
Pushing the algorithm to its limits may hopefully shed light on mathematical patterns that would otherwise not be discernible.
This work offers an effective method for enhancing degradation of dyes and may hopefully be also applied for treatment of other recalcitrant compounds in water and wastewater.
As it is designed to reduce carriage and transmission of Bordetella pertussis, it may hopefully contribute to the ultimate control of pertussis.
The simulation results for multiobjective resource allocation problems (MORAP) shows that genetic algorithms (GAs) may hopefully be a new approach for such kinds of problems.
The simulation results for MORPs shows that genetic algorithms (GAs) may hopefully be a new approach for such kinds of difficult-to-solve problems.
Our opening ceremony (a customary grand event in this part of the world) may, hopefully, be the time to breathe a sigh of relief.
"There is a whole rest of my life once I retire from tennis, whenever that may be – hopefully not for a number of years.
Officials here may search hopefully for any sign of a softening on the part of the White House, but they are not retreating from Mr. Schröder's pledge that Germany will steer clear of an attack on Iraq.
"My whole waking life is all about this [battling the incinerator], so 3 May will hopefully change things".
