This subject has been pretty well covered so how about a summary.
First, it is always better to look at an induction motor as a machine that develops torque and speed. Forget hp. Virtually all three phase induction motors will develop their rated torque (use the common formula T=hp x 5250/base speed) from near zero speed up to the motor's design base speed. That would be 50hz or 60hz generally. As you go above base speed, the torque falls off as the inverse of the overspeed up to a point where the torque starts falling off more rapidly than the overspeed and drops to zero soon after.
Second, in the zero to base speed range, while the magnetics are happy to produce the torque stated above, there are thermal limits in the motor depending on frame size, cooling method, insulation temp limits, etc. that prevent that full torque from being used on a contiuous basis. Motor manufacturers will provide a curve for this derating. This applies to all motors, not just inverter duty.
Third, in the overspeed range there are also some limits. Mechanical strength in the fan and rotor and balance issues may limit overspeed range below the point where the torque drops too low for the load. Bearings for all but 2 pole motors (3000 or 3600rpm) are not an issue since the same bearings are often used on 2,4,and 6 pole motors. This is true for all motors, not just inverter duty types. The manufacturer publishes torque/speed curves for the overspeed range too. Motor life is often improved by running overspeed, not reduced as mentioned above.
Finally, if you absolutely must use horsepower for sizing (always dangerous), you can study the torque/speed curves given above and you will see that, in underspeed, the horsepower (assuming no thermal derating) is a straignt line running from zero at zero speed up to the nameplate horsepower at nameplate speed. In overspeed, the horsepower is also a straight line which runs level from the nameplate horsepower point up to the speed where the torque begins to fall off rapidly. On commodity motors that point can be as low as 80Hz and on inverter duty motors is often guaranteed to be not lower than 120hz or double base speed. Again, use the manufacturers' charts.
Just one footnote: I did not say that you can take 2 pole (3000 or 3600rpm) motors up to double speed. The overspeed range is limited for those motors by mechanical and balance issues. What I said about underspeed, however, applies.
I am quite sure that typical torque/speed curves can be seen on rsdoran's excellent website and certainly can be had from motor manufacturers.
