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Jan Oort was a pioneer in radio astronomy. Wikipedia says:

It has been written that “Oort was probably the first astronomer to realize the importance” of radio astronomy. “In the days before radio telescopes,” one source notes, “Oort was one of the few scientists to realise the potential significance of using radio waves to search the heavens. His theoretical research suggested that vast clouds of hydrogen lingered in the spiral arms of the Galaxy. These molecular clouds, he predicted, were the birthplaces of stars.”

The article includes the image shown below, which is a 21 cm radio map of the Milky Way galaxy. (for more on the transparency of dust at 21 cm see this excellent answer to How was the galactic plane established?

You can also read more about Oort's work during this time in this 1976 AIP Oral History Interview interview.

I'm guessing that the center of the plot is the galactic center and the point at 8 kpc above it is the Earth. What is the reason for the two blank wedges, projecting downward and upward from the Earth? Are they geometrical, blind spots from the few early radio telescopes in the 1950's perhaps, or do they reflect real phenomenon in the galaxy?

The original source is The galactic system as a spiral nebula Oort, J. H.; Kerr, F. J.; Westerhout, G. MNRAS 118, (1958) p. 379

TLDR: these wedges are bits where things are moving around the centre of the galaxy at about the same speed as us, so we can't understand what is there.

As it states on page 4 of the paper you have linked,

the great gap between 315 and 340, where, except at small R, the differential rotation is too small to separate the various arms

The method used to deduce this structure is described on page 2:

Observations in the decimetre continuum can only give the integrated radiation over the line of sight. The 21-cm line gives discrimination in distance. But although the 21-cm observations give discrimination in distance they cannot by themselves provide actual distances. The distance distribution in a given direction can only be inferred from radial velocities. For this we have to suppose that in each part of the Galactic System the average motion of the gas coincides with the circular velocity at the corresponding distance from the centre.

The map is given by combining several observations at different wavelengths - the 'decimetre' gives the total amount of stuff along the line of sight (because it isn't absorbed much along the way), the 21-cm line gives a measure of distance (because it is absorbed so predictably wakened by the amount of stuff it has passed through), and then to we have to assume a model of Keplerian rotation as a guess at how things are moving around the centre of the galaxy. Combining these three things allows you to map out the material even though you are seeing different bits stacked together along your line of sight.

This doesn't work in the blank wedges because the speed of rotation is too similar to ours, so we can't use the rotation velocity to disentangle distances.