Generally, one who eats a food that grows from a tree recites the Beracha of "Bore Peri Ha'etz," and one who eats a food that grows directly from the ground recites the Beracha of "Bore Peri Ha'adama." The question arises, what Beracha does one recite over a vegetable grown in a pot, or over a fruit taken from a tree that grew in a pot?
Some flowerpots have a hole in the bottom and placed on earth, such that the plant grown inside draws its nutrients from the earth in the ground, just like other plants. Halachic sources refer to these pots with the term "Asitz Nakuv." According to all authorities, plants grown in an "Asitz Nakuv" require the same Beracha that would be recited if these plants had been grown normally. Thus, if one eats a vegetable grown in such a pot, he recites "Bore Peri Ha'adama," and if he eats a fruit taken from a tree that grew in such a pot, he recites "Bore Peri Ha'etz."
The more complex question is whether or not the Beracha changes in cases of an "Asitz She'eno Nakuv," plants grown in earth contained in a pot that does not have a hole in the bottom. Since these plants did not grow from the ground or from a tree that grows from the ground one might argue that they do not require the standard Beracha of "Bore Peri Ha'adama" (which literally means, "Who creates the fruits of the ground") or "Bore Peri Ha'etz" ("who creates fruits of the tree"). Indeed, the Haye Adam (Halachic work by Rabbi Avraham Danzig, 1748-1821) ruled (51:17) that over any food grown in such a flowerpot one recites the Beracha of "She'hakol." Even if one grew grain in an "Asitz She'eno Nakuv" and produced bread from that grain, he recites the Beracha of "She'hakol."
Most other authorities, however, disagreed, and maintained that since even plants grown in these kinds of pots are produced from earth, they retain their usual Beracha. This is indeed the ruling of Hacham Ovadia Yosef in his work Hazon Ovadia (Laws of Berachot, p. 112; listen to audio recording for precise citation). Thus, the Beracha required for fruits, vegetables and grain products remains the same if the item was grown in a pot, and no distinction is drawn in this regard between pots with a hole and pots without a hole.
A different question was raised concerning fruits and vegetables grown through hydroponics a system developed by recent technology whereby plants are grown in water, without any earth. Which Beracha does one recite over fruits and vegetables grown through this method?
Hacham Ovadia Yosef (ibid.) rules that such fruits and vegetables cannot be considered as having grown from the ground, and they therefore require the Beracha of "She'hakol." He bases this ruling on the fact that several leading authorities of the previous and current generations including the Hazon Ish, Rabbi Yehiel Michel Tuketchinsky and Rabbi Binyamin Zilber held that the laws of Shemita do not apply to hydroponics. Halacha forbids planting during the Shemita year, and yet the aforementioned authorities permit producing food through hydroponics, as this does not constitute planting. This ruling demonstrates that Halacha does not view these products as "plants," and, as such, one cannot recite over them the Beracha of "Bore Peri Ha'adama" (or, in the case of fruits, "Bore Peri Ha'etz").
Nevertheless, Hacham Ovadia adds, a person who mistakenly recited "Bore Peri Ha'etz" or "Bore Peri Ha'adama" over foods produced through hydroponics has nevertheless fulfilled his obligation, and need not recite "She'hakol" before eating. Furthermore, he noted that when one purchases fruits or vegetables in the market he may assume that they had been grown naturally, and not through hydroponics, as most fruits and vegetables are grown naturally. Hence, unless one knows for sure that a given food had been produced through hydroponics, he should recite "Ha'etz" or "Ha'adama."
Summary: One recites "Ha'etz" or "Ha'adama" over fruits or vegetables grown in flowerpots, even if the flowerpot did not have a hole to allow the plants to draw nutrients from the ground. One who eats fruits or vegetables produced through hydroponics recites the Beracha of "She'hakol"; if, however, he recited "Ha'etz" (in the case of a fruit) or "Ha'adama" (in the case of a vegetable), he has nevertheless fulfilled his obligation.
