What was done
The authors correlated the monthly rate of relative change in normalized difference vegetation index (NDVI), which they derived from advanced very high resolution radiometer (AVHRR) data, with the rate of change in atmospheric CO2 concentration during the natural vegetation growing season within three different eco-region zones of North America (Arctic and Sub-Arctic Zone, Humid Temperate Zone, and Dry and Desert Zone, which they further subdivided into 17 regions) over the period 1982-1992, after which they explored the temporal progression of annual minimum NDVI over the period 1982-2001 throughout the eastern humid temperate zone of North America.

What was learned
Lim et al. report that in all of the 17 regions but one, "δCO2 was positively correlated with the rate of change in vegetation greenness in the following month, and most correlations were high," which they say "is consistent with a CO2 fertilization effect" of the type observed in "experimental manipulations of atmospheric CO2 that report a stimulation of photosynthesis and above-ground productivity at high CO2."  In addition, they determined that the yearly "minimum vegetation greenness increased over the period 1982-2001 for all the regions of the eastern humid temperate zone in North America."

As for the cause of this latter phenomenon, Lim et al. say that rising CO2 could "increase minimum greenness by stimulating photosynthesis at the beginning of the growing season," citing the work of Idso et al. (2000), who discovered that although new spring branch growth of sour orange trees began on exactly the same day of the year in both ambient (400 ppm) and CO2-enriched (700 ppm) open-top chambers, the rate of new-branch growth was initially vastly greater in the CO2-enriched trees.  Three weeks after branch growth began in the spring, for example, new branches on the CO2-enriched trees were typically more than four times more massive than their counterparts on the ambient-treatment trees; while on a per-tree basis, over six times more new-branch biomass was produced on the CO2-enriched trees, before declining to an approximate 80% stimulation typical of the bulk of the growing season.

What it means
By looking for a manifestation of the CO2 fertilization effect at the time of year it is apt to be most strongly expressed, Lim et al. may well have found it.  Between 1982 and 2001, for example, the air's CO2 concentration rose by approximately 30 ppm.  From Idso et al.'s findings of (1) more than a 300% initial increase in the biomass of new sour orange tree branches for a 300-ppm increase in the air's CO2 concentration and (2) more than a 500% initial increase in per-tree new-branch biomass, we calculate that yearly minimum greenness should have increased by something between something just over 30% and something just over 50%, if other woody plants respond to atmospheric CO2 enrichment as sour orange trees do; and when we calculate the mean 19-year increase in NDVI for the seven regions for which Lim et al. present data, we get an increase of something just over 40%, indicative of the fact that Lim et al.'s data are not only qualitatively consistent with their hypothesis, they are right on the money quantitatively as well.

Reference
Idso, C.D., Idso, S.B., Kimball, B.A., Park, H., Hoober, J.K. and Balling Jr., R.C.  2000.  Ultra-enhanced spring branch growth in CO2-enriched trees: can it alter the phase of the atmosphere's seasonal CO2 cycle?  Environmental and Experimental Botany 43: 91-100.